Question

Select the correct answer.

Answer 1

Answer:

B

Step-by-step explanation:

The sum to n terms of a geometric series is

$S_{n}$ = $\frac{a(1-r^{n}) }{1-r}$

where a is the first term and r the common ratio

Here a = 6144 and r = $\frac{a_{2} }{a_{1} }$ = $\frac{3072}{6144}$ = $\frac{1}{2}$ , then

$S_{10}$ = $\frac{6144(1-(\frac{1}{2}) ^{10}) }{1-\frac{1}{2} }$

     = $\frac{6144(1-\frac{1}{1024}) }{\frac{1}{2} }$

     = 12288(1 - $\frac{1}{1024}$ ) ← distribute

     = 12288 - 12

     = 12276 → B