







Loan payment formula 
20190224 

From Kenneth:
I have a question regarding the loan payment formula shown below.
Calculating the Payment Amount per Period
The formula for calculating the payment amount is shown below.
Simple Amortization Calculation Formula
A = P X r(1 + r)n over (1 + r)n  1
where
A = payment Amount per period
P = initial Principal (loan amount)
r = interest rate per period
n = total number of payments or periods
Is this formula/calculation a condensed version of a longer calculation? I am curious to know how the (1 +r)n  1 was developed from the longer calculation. For example, r(1 + r)n may have been (r + rn)n. The n's are exponents.
I thank you for whatever helpful explanation that may be provided.
Kenneth Answered by Harley Weston. 





A geometric series 
20180313 

From nathi: Hi I am really struggling with this question please help !!!!
a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year.
assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence.
A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres.
The maximum height part is not answered. Answered by Penny Nom. 





Triakis 
20160627 

From Gordon: Some authorities treat "triakis" (and related terms "dyakis", "tetrakis", etc.) as attached prefixes; others treat them as separate adjectives. Thus I see one of the Catalan solids described as both "triakistetrahedron" and "triakis tetrahedron". Which usage is correct? Answered by Chris Fisher. 





A geometric progression 
20160303 

From Pauline: A woman measures the height of her child at birth and at monthly intervals afterwards.The child's height increases by 5% per month. Find the number of measurements she has made before the child's height is twice what it was at birth Answered by Penny Nom. 





A geometric sequence 
20150419 

From Delfina: In a geometric sequence the second term is 15 and the fifth term is 405. Find the sum of the first eight terms Answered by Penny Nom. 





Find the nth term 
20141026 

From Kenneth: According to the pattern of the following sequence. Find it's nth term:
3,9,27,81,243,.......... Answered by Penny Nom. 





9,4,6,8,3,... 
20140331 

From Alynna: You are given the following pattern: 9,4,6,8,3,...
Create a formula for the nth figure.
I have trouble finding the formula, I need help trying to find it. Answered by Penny Nom. 





An infinite geometric series 
20131224 

From Muhammad: The sum of an infinite geometric series is 15 and the sum of their squares is 45. Find the series Answered by Penny Nom. 





A geometric sequence 
20130716 

From Relebohile: Find the n^th term of 3,6,9,12,24,48... Answered by Penny Nom. 





A geometric sequence 
20120610 

From vicki: The sum of the first three terms of a geometric sequence of positive integers is equal to seven times the first term, and the sum of the first four terms is fortyfive. What is the first term of the sequence? Answered by Penny Nom. 





A geometric sequence 
20120224 

From Camille: Find x if the sequence 5,10,x+2 is geometric. Answered by Penny Nom. 





A tree growth modelled by a geometric series 
20120208 

From Steph: Hi I am really struggling with this question please help !!!!
a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year.
assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence.
A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres Answered by Penny Nom. 





1 + 3 + 3^2 ...+3^(n1) = 3^n  1/2 
20120127 

From Vicki: I am trying to find out how to do show how this proof was worked.
Here is the end result 1 + 3 + 3^2 ...+3^(n1) = 3^n  1/2
This equation was used to find the number of white triangles in the Sierpinski Triangle Answered by Walter Whiteley. 





Mean and Average 
20120103 

From john: what is the difference between average and mean Answered by Robert Dawson. 





An imaginary infinite geometric tree 
20110218 

From Elise: An imaginary infinite geometric tree grows 1m the first day.
2nd day 2 branches and right angles to each other and each 0.5 m long.
3rd day two new branches at ends of each of previous days' 2 branches, again at right angles, and only .25m long each.
And so on, infinitely.
Q: Use relationships of rightangled triangles and high school level knowledge of geometric series to show
the tree height is limited to (4 + sqrt2)/3 m and width to (2(sqrt2 + 1))/3 m. Answered by Robert Dawson. 





A geometric progression 
20101215 

From Abeth: find the value of x so that 2(x1), x+3, x will be a geometric progression. Answered by Penny Nom. 





The value after 30 years 
20101215 

From Abeth: At the end of every year, the owners of a building which costs 2, 500, 000 pesos deducts 15% from its carrying value as estimated at the beginning of the year. find the estimated value at the end of 30 years. Answered by Penny Nom. 





A geometric progression 
20100430 

From Kalyani: sum of infinite geometric progression is 9 and common ratio is 1/10
then sum up to 8 terms is? Answered by Chris Fisher. 





A geometric sequence 
20100413 

From glen: A geometric sequence has a first term of 0.1024, a second term of 0.256,
and a middle term of 156.25. how many terms are there in the whole
sequence?
i know that r=2.5 but i dont know how to find how many terms there are. Answered by Penny Nom. 





A geometric sequence 
20100222 

From Kelsey: _, 2, _, _, 250, _
i don't know how to fill in the missing terms Answered by Penny Nom. 





An infinite geometric series 
20090518 

From terri: find the sum of the infinite geometric series
14 7 +7/2 7/4 +.....
A. 7007/13 B. 2002 C. 28/3 D.5005/7 Answered by Stephen La Rocque. 





A geometric progression 
20090516 

From sweta: find the ratio of GP if the first term is 1 and the sum of third and fifth term is 90. Answered by Penny Nom. 





A geometric construction 
20081017 

From M: Given any 3 parallel lines on a plane, how to construct an equilateral triangle with each vertex on each line? Answered by Chris Fisher. 





0.151515...=15/99 
20080908 

From Emma: This week, my Algebra teacher told us about the pattern between infinitely repeating
decimals and their corresponding fractions.
(ex. .2222222...= 2/9, .151515...=15/99, 456456456...=456/999, etc.)
I was just wondering the reason why this pattern occurs.
Is there a certain element that causes this pattern to occur?
Thanks
Emma Answered by Penny Nom. 





Proofs 
20080726 

From Taylor: when doing a proof, how do i figure out the steps in which i find the statements? i find the reasons pretty easily but i do not understand how to get the proving part. that would be great if you can help me! Thanks Answered by Victoria West. 





Demographics 
20080725 

From shahrukh: Each year for 10 years ,the population of a city increased by 5% of its value in the previous year.
If the initial population was 200 000 ,what was the population after 10 years ?? Answered by Penny Nom. 





Geometric shapes that are the same 
20080609 

From tia: what is the name used for shapes that are exactly the same? Answered by Harley Weston. 





Geometric sequences 
20080608 

From Rita: A geometric sequence is given. Find the common ratio and write out the first four terms.
(1) {(5)^n}
(2) {(2^n)/(3^(n  1)} Answered by Penny Nom. 





A parallel line to a given line 
20080412 

From john: A parallel line to a given line through a given point not on the a given line Answered by Harley Weston. 





The nth term 
20071018 

From shannon: Ok , what i am having problems with is the nth term. I get how the numbers come together, but i am having trouble with finding the nth term. Answered by Penny Nom. 





Finding a geometric mean and taking its antilog 
20070827 

From Jack: Would like to know the basic geometric mean calculation. Also how would I take the antilog from this number? Answered by Stephen La Rocque. 





Applications of sequences and series 
20070827 

From Trish: I'm a grade 12 learner working on a math project based on sequences and series. I'd like to know the different types of sequences and series such as fibonacci, fourier, farey, etc.
I've already used the Fibonacci Sequence and Harmonic Series
and need two more.
The simpler the sequence or series type the better.
I'd also like to know in which nonmathematical areas use sequences and series
and how.
Areas such as engineering or science. Answered by Penny Nom. 





A sequence of circles 
20070611 

From Ann: Please help with solving the following problem!!!
A circle is inscribed in an equilateral triangle with a side of length 2.
Three circles are drawn externally tangent to this circle and internally
tangent to 2 sides of the triangle. 3 more circles are drawn externally
tantgent to these circles and internally tangent to 2 sides of the triangle. if
this process continued forever, what would be the sum of the areas of all the
circle? the answer 1 parent came up with was Pie over 2, but we don't
know how he did it. Can you please show the work or explain the answer to
this problem?
Thank you
Ann
p s my daughter is in 9th grade math. Answered by Steve La Rocque, Chris Fisher and Penny Nom. 





Arithmetic means and geometric means 
20070404 

From Dani: Hi!
I was just wondering why the arithmetic mean of sets of numbers is larger than the mean proportional of the same numbers?
Thanks!
Dani Answered by Haley Ess. 





A geometric series 
20070403 

From jessica: If a geometric series includes 5418+62 as its fifteenth through eighteenth terms, find the sum of the second through the fifth term, inclusive. Answered by Stephen La Rocque. 





The nth term 
20070213 

From Sarah: I am having difficulty in finding the nth term for 7,49,343,2401. Could you please help me in finding the correct answer? Answered by Stephen La Rocque. 





Find the total distance the swing traveled before it stopped. 
20061217 

From Leah: Rebecca's little sister liked for her to push her in the swing at the park. The other day Rebecca pulled the swing back and let it go. She would have kept pushing, but she suddenly saw a friend at the other end of the park. The swing traveled a total distance of 10 feet before heading back the other way. Each swing afterwards was only 80% as long as the previous one. Find the total distance the swing traveled before it stopped. Answered by Penny Nom. 





A geometric sequence 
20061128 

From Jillian: Find x so that 2x, x + 5, x  7 are consecutive terms of a geometric sequence. Answered by Stephen La Rocque. 





Geometric sequence and basic functions (graphs) 
20060420 

From Marlene: Which of the basic functions is related to the geometric sequence:
Linear, Quadratic, Rational, or Exponential?
Can you give me an example of how it would be used in normal life? Answered by Stephen La Rocque. 





Arithmetic and Geometric Sequences 
20060419 

From Skye: If the 1st, 4th, and 8th terms of an arithmetic sequence are consecutive terms in a geometric sequence, find the common ratio of the geometric sequence. Answered by Stephen La Rocque. 





Sum of a Geometric Sequence 
20060411 

From Andre: In a particular geometric sequence, U3=3.6 and U10=12.9. Find S16 and S17. Answered by Stephen La Rocque. 





An isosceles triangle 
20051114 

From Chris: PX and QY are attitudes of acute triangle PQR, and Z is the midpoint of PQ. Can you write a proof that triangle XYZ is isosceles? Answered by Chri Fisher. 





A geometric sequence 
20050621 

From A student:
The first three terms of a geometric series are 3(q+5), 3(q+3), (q+7) respectively.
Calulate the value of q. Answered by Penny Nom. 





A geometric proof 
20041211 

From Hanna: Given: ABCD is a quadrilateral;
Prove: ABCD is a parallelogram Answered by Penny Nom. 





Geometric sequence 
20041204 

From Lesa: Find a formula for the geometric sequence: (√3  √2), (4  √6), (6√3  2√2), … Answered by Penny Nom. 





A geometric sequence 
20040413 

From Michael: In a geometric series, the sum of the 2nd and 3rd terms is 60, and the sum of the 3rd and 4th terms is 240. Find the sum of the first 7 terms. Answered by Penny Nom. 





A worm crawling home 
20040218 

From Cindy: A worm is crawling to his home which is one meter away. The longer he crawls the weaker he gets and the less he can crawl the next day. If he crawls within 1/3000 of a meter of his home, he will find food. He must eat within twelve days. The first day he crawls 1/2 meter. The second day he crawls 1/4 meter. The third day he crawls 1/8 of meter. This pattern continues for twelve days. Make a Chart that shows the distance he has covered at the end of each day and the total he has covered at the end of each day. Does he make it to the Food in time? Answered by Penny Nom. 





Geometric sequences 
20040203 

From Alan: hello, I am a junior in precalculus. we started working on geometric sequences today, it makes perfect sense on how it works. but why is it called that? if you could send me an answer to why geometric sequences have that name, I would be much appreciative. Answered by Chris Fisher. 





8 faces, 12 vertices, and 18 edges 
20030422 

From Thomas: I would like to know the proper name for this geometrical solid. It has 8 faces, 12 vertices, and 18 edges? Answered by Penny Nom. 





A bouncing ball 
20021214 

From Eman:
Q : When a childís ball is dropped from a height h metres on to a hard, flat floor, it rebounds to a height of 3/5h metres. The ball is dropped initially from a height of 1.2m.  Find the maximum height to which the ball rises after two bounces.
 Find the total distance that the ball has traveled when it hits the floor for the tenth time.
 Assuming that the ball continues to bounce in the same way indefinitely, find the total distance that the ball travels.
Answered by Penny Nom. 





A geometric sequence 
20021202 

From Wanda: the fifth term of a geometric sequence is 5/16. the common ratio is 1/2. What are the first four terms of the sequence. Answered by Penny Nom. 





My salary is doubled everyday for 30 days 
20020117 

From Kanishk: I recieve 1 penny the 1st day, 2 pennies the 2nd day, and my salary is doubled everyday for 30 days. How much money will I have by the end of the 30 day time period? (Is there a way of solving this problem without a chart?) Answered by Penny Nom. 





A geometric series 
20011024 

From Tashalee: The sum of the first 3 terms of a geometric series is 13. The sum of their reciprocal is 13/9. how do you find the first three terms? Answered by Penny Nom. 





The average of two polygons 
20011023 

From Irene: How can I prove that the average of two polygons will give me another one? Answered by Walter Whiteley. 





Geometric and arithmetic sequences 
20010126 

From Garry: what are the equations for geometric and arithmetic sequences? also, what are the equations for finding the sums of those series? Answered by Leeanne Boehm and Penny Nom. 





Power series representations 
20001127 

From Grace: Is there a systematic way of finding a power series representation of a function? I understand that you have to manipulate the function so that it is of the form 1/(1x), but beyond that I am lost. Answered by Harley Weston. 





Comparing an integral and a sum 
20001121 

From Douglas Norberg: A fellow teacher asked me about a problem she wanted to give to her students. It involved whether to take a million dollars or a penny doubled a number of times. I was able to determine the number must have been .01 * 2^{30} which is about $10 million and a lot more than $1 million. To check that I was right I used a spreadsheet and did a Riemann sum. When I finished I reasoned that I had done the task in several steps and I could have done it in 1 step. Thus I integrated .01 * 2^{x} from 0 through 30 but the number I got was $15,490,820.0324. Why the difference? Answered by Harley Weston. 





Infinite Geometric Series 
20001110 

From Sam Carter: I ran into a problem when studying how to find the sum of an infinite geometric series. My math book attempts to explain the concept by giving formulas involving sigma and r, but it does not really explain how to go about finding the sum of an infinite geometric series. If you could either help me with this or point me in the direction of an informative website that could help me, I'd appreciate it. Answered by Harley Weston. 





Geometric sequences 
20000411 

From Jodie: I am in a grade ten principles class and was taught how to do geometric sequences and series but no one in my class understood what we were taught. Our teacher is one of few to use the new curriculum which used to be the grade twelve curriculum. Could you please explain to me how to do geometric sequences and how to find the different terms and sums. Thank you very much! Answered by Harley Weston. 





Geometrical solids 
20000315 

From Sarah:
 What geometrical solid has 8 edges and 5 vertices?
 What geometrical solid has 12 edges that are all the same length?
Answered by Walter Whiteley. 





Pyramids and prisms 
20000118 

From Tyler: What's the definition of a Triangular Prism and a Triangular pyramid. Answered by Penny Nom. 





Dotted graph paper 
19990408 

From Bridget Winward: A teacher at our school is trying to locate dotted graph paper online or in print. His class would like to make three dimensional, geometerical drawings. Please let us know if you have a good source. Answered by Jack LeSage. 





Two sides and a bisectrix. 
19981111 

From Victor Grinshtein: I am looking for someone who can tell me how to construct a triangle by 2 sides and a bisectrix using a compass and a ruler. Answered by Chris Fisher. 





A Pattern 
19980914 

From Krystin: Question: 1=1x1 1+2+1=2x2 1+2+3+2+1=3x3 draw a series of diagrams to illustrate the above pattern Answered by Penny Nom. 





Sequences and series 
19980527 

From Michael Le Francois: The sum of the first ten terms of an arithmetic series is 100 and the first term is 1. Find the 10th term. The common ratio in a certain geometric sequence is r=0.2 and the sum of the first four terms is 1248 find the first term. Answered by Penny Nom. 

