Question

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

Answer 1

B. 12,276

Explanation:

We have the following geometric sequence:

`6144+3072+1536+768...`

We can determine the pattern (ratio) as follows:

`\begin{gathered} (6144)/(3072)=2 \\ \\ (3072)/(1536)=2 \\ \\ (1536)/(768)=2 \end{gathered}`

We calculate the other 6 terms to determine the sum:

`\begin{gathered} (768)/(2)=384 \\ \\ (384)/(2)=192 \\ \\ (192)/(2)=96 \\ \\ (96)/(2)=48 \\ \\ (48)/(2)=24 \\ \\ (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)=(6144\left(1-\left((1)/(2)\right)^(10)\right))/(1-(1)/(2)) \\ \\ S_(10)=12276 \end{gathered}`

So the correct answer is B. 12,276