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arithmetic progression

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1 + 2 + 3 + ... + (2n - 1) 2015-01-01
From Brian:
Hi Maths Central
My wife presented me with a query which may have a simple answer, but one that I can’t deduce or explain.

Take the string of numbers, n=1,2,3,4,5…
It seems that n(2n-1) = Sum((1…..(2n-1))
e.g. for n=5, both 5 x 9 and Sum(1….9) equal 45, and so on for other values of n.

Could you please provide an explanation? Does it have an underlying reason and a name?

Look forward to your response.
Brian

Answered by Penny Nom.
An arithmetic progression 2014-11-19
From Gbenga:
In an A.P the difference between 8th and 4th term is 20. The 8th term is 1\2 times the 4th term . Find arithmetic progression..
Answered by Penny Nom.
The sum of the first 50 terms of an arithmetic progression 2014-07-26
From Joshua:
Hello ...my is Joshua...I'm a grade 11 student...I got a question

Calculate the sum of the first 50 terms of an arithmetic progression: 112:98:84

Answered by Penny Nom.
An arithmetic progression 2014-03-31
From Japheth:
The 3rd term of an A.P is 10 more than the first term while the fifth term is 15 more than the second term. Find the first term?
Answered by Penny Nom.
An arithmetic sequence 2014-01-06
From paris:
find the twenty-fifth term of an arithmetic sequence whose first term is 12 and whose common difference is -6
Answered by Penny Nom.
An Arithmetic Progression 2013-10-08
From collins:
In an A.P. the difference between the 8th and 4th term is 20 and the 8th is one and half times the 4th term... what is the common difference and the first term
Answered by Penny Nom.
The sum of all whole numbers from 1 to X 2013-09-06
From Tim:
How do I develop a rule for the sum of all whole numbers from 1 to X when I have no idea how to do this
Answered by Penny Nom.
An arithmetic progression 2013-07-06
From ashok:
the 4th and 10th term a.p respectively 7 and 19 find its 15th term.....
Answered by Penny Nom.
An arithmetic progression 2013-02-06
From loberto:
the 3rd term of an a.p is 10more than the 1st term,while the 5th term is 15more than the 2nd term,find the sum of the 8th and 15th terms of the a.p if the 7th term is 7times the 1st term
Answered by Penny Nom.
An arithmetic progression 2012-08-22
From A student:
the 3rd term of an A.PPP is 10 more than the first term while the 5th term is 15 more than the second.find the sum of the 8th and 15th terms if the 7th term is 7 times the first term.
Answered by Penny Nom.
The 3rd term of an A.P is 10 more than the first term 2011-11-29
From Olaniyan:
the 3rd term of an A.P is 10 more than the first term while the fifth term is 15 more than the second term. Find the sum of the 8th and 15th terms of the A.P if the if the 7th term is 7 times the first term.
Answered by Penny Nom.
4 + 10 + · · · + (6n − 2) 2010-04-21
From Lan:
Find the sum 4 + 10 + · · · + (6n − 2). The answer is 3(n^2) + n. How?
Answered by Penny Nom.
Arithmetic progressions 2006-01-31
From A student:
1)the sum to n terms of a particular series is given by Sn=17n-3n2

a)find an expression for the n term of the series
b)show that the series is an arithmetic progression

2)a particular arithmetic progression has a positive common difference and is such that for any three adjacent terms ,three times the sum of their squares exceeds the square of their sum is 375.Find the common difference


Answered by Penny Nom.
Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: 2005-07-18
From Ladis:
Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: p=p, q=p+d and r= p+2d. Prove that d is divisible by 6.
Answered by Chris Fisher.
An arithmetic progression 2004-12-24
From A student:
the 4th and 5th term of an arithmetic progration 47 and 52 respactively find
a)d
b)a1
c)a50

Answered by Penny Nom.
1+3+5+...+(2n+1) 2004-09-10
From Emma:
Prove that 1+3+5+...+(2n+1)= (n+1)2
Answered by Penny Nom.
The sum of some positive integers 2004-06-07
From A student:
Find the sum of all positive integers not greater than 10000 that are divisible by neither 3 nor 7.
Answered by Penny Nom.
7+8+9+...+1000 2002-09-11
From Shirley:
My question is what is the formula for adding up numbers when you don't start with number 1? For example 3 + 4 + 5 + 6 = 18. But how could you arrive at the answer without adding all the numbers?
Answered by Penny Nom.
Arithmetic progressions 2002-04-24
From David:
I have been searching everywhere for the formula to mathamatical progression.
Answered by Penny Nom.
Arithmetic sequences 2001-09-10
From Rachel:
I can't seem to figure out a problem that deals with arithmetic sequencing. This is the question: The 5th term in an arithmetic sequence is 1/2, and the 20th term is 7/8. Find the first three terms of the sequence. I attempted this problem with the formula: An = a + (n-1)d (where the n represents the nth term, a is the first term, and d represents the common difference) I keep getting -9.5 for the first number, and then 3/120 as the common difference between the numbers. But as I have figured it, the sequence is getting greater and greater, and my data does not go with the terms given.
Answered by Penny Nom.
Arithmetic Progressions 1998-11-12
From Gerry Boser:
It has been years since I was in school and I can't remember if there is a formula for the following problem:

If you deposit $1.00 on the first day of the month, $2.00 on the second day, $3.00 on the third day . . $31.00 on the last day of the month, how much do you have in the bank?

Now will this formula also work if it was, $0.25 (then day two you would deposit 2x $0.25 or $0.50, day three you would deposit 3x $0.25, $0.75. . . ). Will it work with any denomination??

Thank you for your time. I promise I'll write this one down for future reference. . .
Answered by Penny Nom.

Dividing a Class 1998-10-01
From Tom Barker:
My eighth grade niece called with the following homework problem:

A teacher wanted to divide her class into equally numbered groups. She tried to divide the class into groups of two, but was one student short. She tried to divide the class into groups of five, but was one student short. She tried to divide the class into groups of seven and was successful. What is the least number of students that were in her class?

I know the answer is 49, but don't know how to prove it. I must be getting old if I can't solve eighth grade math problems. Your assistance would be appreciated.
Answered by Penny Nom.

 
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