Question

Use sigma notation to represent the following series for the first 10 terms. 3+ (-6) +12+(-24)

Answer 1

Answer: - 1023

Explanation:

Given

Sequence is
`3+(-6)+12+(-24)...`

The following sequence is a geometric series with common ratio
`r=-2`

first term
`a=3`

`Sum=\sum _(i=1)^(n)ar^(n-1)=(a(1-r^n))/(1-r)`

`Sum=\sum _(i=1)^(n)3(-2)^(n-1)=(3(1-(2)^10))/(1+2)`

`Sum=\sum _(i=1)^(n)3(-2)^(n-1)=-1023`