Question

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

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

Answer:

C) 65535.

Step-by-step 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) = $\frac{a_{2}}{a_{1} }$

r =  $\frac{12}{3}$.

r = 4.

Sum = $a_{1} \frac{(1-r^{n})}{1-r}$

Then,

$S_{8}$ =  $3 \frac{(1-4^{8})}{1-4}$.

$S_{8}$  =  $\frac{-196605}{-3}$.

 $S_{8}$  = 65535.

Therefore, C) 65535.