Question

What is the sum of the first 10 terms of this geometric series?

Answer 1

ANSWER:

B. 12,276

STEP-BY-STEP EXPLANATION:

We have the following geometric sequence:

$6144+3072+1536+768...$

We can determine the pattern (ratio) as follows:

$\begin{gathered} \frac{6144}{3072}=2 \\ \\ \frac{3072}{1536}=2 \\ \\ \frac{1536}{768}=2 \end{gathered}$

We calculate the other 6 terms to determine the sum:

$\begin{gathered} \frac{768}{2}=384 \\ \\ \frac{384}{2}=192 \\ \\ \frac{192}{2}=96 \\ \\ \frac{96}{2}=48 \\ \\ \frac{48}{2}=24 \\ \\ \frac{24}{2}=12 \\ \\ \text{ Now, we calculate the sum as follows:} \\ \\ 6144+3072+1536+768+384+192+96+48+24+12=12276 \\ \\ \text{ We can also determine it by means of the formula, since the ratio would be r = 1/2 and n = 10} \\ \\ S_{10}=\frac{6144\left(1-\left(\frac{1}{2}\right)^{10}\right)}{1-\frac{1}{2}} \\ \\ S_{10}=12276 \end{gathered}$

So the correct answer is B. 12,276