Question

Evaluate using the finite geometric sum formula

Answer 1

The correct choice is b. -18.703

Answer 2

`S_9=-18.703`.

Explanation:

The given series is,

`\sum_(i=1)^9(-(1)/(2))^(i-1)`

When we substitute
`i=1`, we get the first term, which is
`a_1=-28(-(1)/(2))^(1-1)`

This implies that,

`a_1=-28(-(1)/(2))^(0)`

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

The common ratio is

`r=-(1)/(2)`

The finite geometric sum is given by the formula,

`S_n=(a_1(r^n-1))/(r-1) , -1\:<\:r<\: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=(-28((-(1)/(2))^9-1))/(-(1)/(2)-1)`.

`S_9=(-28((-(1)/(2))^9-1))/(-(1)/(2)-1)`.

`S_9=(-28((-(1)/(512))-1))/(-(3)/(2))`.

`S_9=(-28(-(513)/(512)))/(-(3)/(2))`.

`S_9=-28((171)/(256))`.

`S_9=-(1197)/(64)`.

`S_9=-18.703`.

The correct answer is B