Question

Evaluate using the finite geometric sum formula

Answer 1

Answer:

$S_9=-18.703$.

Step-by-step explanation:

The given series is,

$\sum_{i=1}^9(-\frac{1}{2})^{i-1}$

When we substitute $i=1$, we get the first term, which is $a_1=-28(-\frac{1}{2})^{1-1}$

This implies that,

$a_1=-28(-\frac{1}{2})^{0}$

$a_1=-28(1)=-28$.

The common ratio is

$r=-\frac{1}{2}$

The finite geometric sum is given by the formula,

$S_n=\frac{a_1(r^n-1)}{r-1} , -1\:$.

Since there are 9 terms, we find the sum of the first nine terms by putting $n=9$ in to the formula to get,

$S_9=\frac{-28((-\frac{1}{2})^9-1)}{-\frac{1}{2}-1}$.

$S_9=\frac{-28((-\frac{1}{2})^9-1)}{-\frac{1}{2}-1}$.

$S_9=\frac{-28((-\frac{1}{512})-1)}{-\frac{3}{2}}$.

$S_9=\frac{-28(-\frac{513}{512})}{-\frac{3}{2}}$.

$S_9=-28(\frac{171}{256})$.

$S_9=-\frac{1197}{64}$.

$S_9=-18.703$.

The correct answer is B

Answer 2

Answer:

The correct choice is b. -18.703