Question

(08.04 MC
Find the sum of the geometric sequence 3, 15, 75, 375, ... When there are 8 terms and select the correct answer below.

Answer 1

Answer:

The sum of next 8 terms is 292,968

Step-by-step explanation:

Here, the sequence is 3, 15, 75 , ...

Since the given term is in  geometric progression, so

$r = \frac{a_2}{a_1}   = \frac{a_3}{a_2}$

And here, r = 15/ 3 = 5

So, a = 3

r = 5

n = 8

So, sum of n terms of G. P $S_n= \frac{a(r^{n} -1)}{(r-1)}$

or, $S_8= \frac{3(5^{8} -1)}{(5-1)}$

                  = 292,968

Hence, the sum of next 8 terms is 292,968.