Question

What is the sum of the first seven terms of the geometric series? 3 + 12 + 48 + 192 + ... 4,372 12,288 16,383 65,535

Answer 1

16,383 or C

Explanation:

Answer 2

Option 3rd is correct.

Explanation:

Given: 3 + 12 + 48 + 192 + .......

We have to find : Sum of first seven term of the given Geometric series.

First term , a = 3

Common ratio , r =
`(12)/(3)=4`

Sum of the n term of series,
`S_n=(a(1-r^n))/(1-r)`

So,

`S_7=(3(1-4^7))/(1-4)`

`S_7=(3(1-4^7))/(-3)`

`S_7=-(1-16384)`

`S_7=-(-16383)`

`S_7=16383`

Therefore, Option 3rd is correct.