Question

Evaluate the series 4-2 1-0.5 0.25 to s10. round to the nearest tenth.

a. 5.50
b.-2.75
c.2.75
d. 2.66

Answer 1

If we're talking about series, we're talking about a summation.
This is a geometric series, so we will be using the sum to n terms of a geometric series given by:


`S_n = (a(1 - r^(n)))/(1 - r)`, where a is the first term, r is the common ratio, and n is the number of terms.

Now, we know the first term is 4.
We know the ratio is
`-(1)/(2)`
And we are finding to the 10th term.

Plugging everything into the equation:

`S_10 = (4[1 - (-(1)/(2))^(10)])/(1 + (1)/(2))`

After this, we get: 2.6640625... ≈ 2.66 (ie D)