 |
| ||
| |||
|
| Math Central | Quandaries & Queries |
|
Question from vicki, a teacher: I am a 6th grade math teacher back in school after 25 years of teaching. I have forgotten sooo much. My professor gave me this question that I have no idea how to solve. If you would, please explain in elementary terms. Thank you. |
Hi Vicki,
A geometric sequence has the form
\[a, ar, ar^2, ar^3, ...\]
for some numbers $a$ and $r.$ The fact that "The sum of the first three terms of a geometric sequence of positive integers is equal to seven times the first term" tells you that
\[a + ar + ar^2 = 7a.\]
You can divide both sides of this equation by $a$ to obtain
\[1 + r + r^2 = 7.\]
Solve this quadratic for $r.$ There are two solution but you need the one that is positive.
Now take the second fact "and the sum of the first four terms is forty-five" and use it to write an equation. Substitute the value you found for $r$ and solve for $a.$
I hope this helps,
Penny
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.