Question

Find the sum of a geometric series with a1=-96 and r=-1/2 and n=5

Answer 1

The sum of the series is: -66

Explanation:

We can use the formula for a partial sum
`S_n` of a geometric series of n terms, with first term
`a_1` and ratio r:

`S_n=(a_1(1-r^n))/(1-r)`

which in our case translates into:

`S_n=(a_1(1-r^n))/(1-r)\\S_5=(-96(1-(-(1)/(2)) ^5))/(1-(-(1)/(2)) )\\S_5=(-96(1+(1)/(32) ))/(1+(1)/(2) )\\S_5=(-96((33)/(32) ))/((3)/(2) )\\S_5=-(96*11)/(16) \\S_5=-66`