# Math Help - Geometric sequence question.

1. ## Geometric sequence question.

The first term of a finite geometric series is 6 and the last term is 4374. The sum of all terms is 6558. Find the common ratio and the number of terms in the series.

So i get that T1= 6.So, a=6. Sn= 6558. how to find r?

2. ## Re: Geometric sequence question.

What is the formula for the sum of a geometric series?

3. ## Re: Geometric sequence question.

If $t_1 = a$, $t_2 = ar$, $t_3 = ar^2$, ..., $t_n = ar^{n-1}$ and $S_n = t_1 + t_2 + \dots + t_n$, then, according to the standard formula for the sum of geometric progression, we get

$S_n = \frac{a(r^n-1)}{r-1}=\frac{ar^n-a}{r-1}=\frac{rt_n-t_1}{r-1}$

from where

$r=\frac{S_n-t_1}{S_n-t_n}=\frac{S_n-t_1}{S_{n-1}}$.

4. ## Re: Geometric sequence question.

Not using any memorized formulas, just thinking about it:

Given that 6r^n = 4374, divide through by 6 to get r^n = 729. Note that 729 = 27^2, or 9^3, or 3^6; so the answer must be that either r=27 and n=2, r=9 and n=3, or r=3 and n=6. See which one results in a series whose sum of terms 6 + 6r + 6r^2 + ...6r^n = 6558.