The sum of the first 3 terms of a geometric progression is 13 times its first term.Find the possible values of the common ratio of the geometric progression.

Printable View

- Dec 23rd 2009, 07:22 AMmastermin346Progressions
The sum of the first 3 terms of a geometric progression is 13 times its first term.Find the possible values of the common ratio of the geometric progression.

- Dec 23rd 2009, 07:27 AMmathaddict
- Dec 23rd 2009, 08:08 AMe^(i*pi)
- Dec 23rd 2009, 08:38 AMSoroban
Hello, mastermin346!

Quote:

The sum of the first 3 terms of a geometric progression is 13 times its first term.

Find the possible values of the common ratio of the geometric progression.

The first three terms are: .$\displaystyle a,\:ar,\:ar^2$

Their sum is 13 times the first term: .$\displaystyle a + ar + ar^2 \:=\:13a$

We have: .$\displaystyle r^2 + r - 12 \:=\:0 \quad\Rightarrow\quad (r - 3)(r + 4) \:=\:0$

Therefore: .$\displaystyle r \;=\;3\text{ or }-4$