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 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 a_{1} 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 a_{1} using the formula: $a_n = a_1 r^{n - 1}$

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

With your a_{1} and r known, you can now calculate the sum S_{5}.

MATHalino

The formula for the sum of the first

nterms 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

a_{1}and the common ratior.To find the common ratio use the formula

$a_n = a_m r^{n - m}$

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

With

rknown, you can solve fora_{1}using the formula:$a_n = a_1 r^{n - 1}$

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

With your

a_{1}andrknown, you can now calculate the sumS_{5}.