Question

What is the sum of the geometric sequence 3, 12, 48, ... if there are 8 terms?

A. 21,845
B. 43,690
C. 65,535
D. 87,380

Answer 1

`S_8=3+12+48+\cdots+12288+49152`

`S_8=3(4)^0+3(4)^1+3(4)^2+\cdots+3(4)^6+3(4)^7`

`4S_8=3(4)^1+3(4)^2+3(4)^3+\cdots+3(4)^7+3(4)^8`


`S_8-4S_8=-3S_8=3(4)^0-3(4)^8`

`-3S_8=3(1-4^8)`

`S_8=4^8-1`

`S_8=65535`

Answer 2

C) 65535.

Explanation:

Given : sequence 3, 12, 48, ...if there are 8 terms.

To find : What is the sum of the geometric sequence.

Solution : We have given that 3, 12, 48, ......

We need to find 8th term of sequence.

Geometric ratio (r) =
`(a_(2))/(a_(1) )`

r =
`(12)/(3)`.

r = 4.

Sum =
`a_(1) ((1-r^(n)))/(1-r)`

Then,

`S_(8)` =
`3 ((1-4^(8)))/(1-4)`.

`S_(8)` =
`(-196605)/(-3)`.

`S_(8)` = 65535.

Therefore, C) 65535.