# Geometric progression

Find the sum of the first 5 terms of the geometric progression if the third term is 144 and the sixth term is 456.? ### The formula for the sum of

The formula for the sum of the first n terms of geometric progression is
$S_n = \dfrac{a_1(1 - r^n)}{1 - r}$

All we need to do is to find the first term a1 and the common ratio r.

To find the common ratio use the formula
$a_n = a_m r^{n - m}$

$a_6 = a_3 r^{6 - 3}$

With r known, you can solve for a1 using the formula:
$a_n = a_1 r^{n - 1}$

$a_6 = a_1 r^{6 - 1}$

With your a1 and r known, you can now calculate the sum S5.

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