Question

What is the sum of the geometric series?

Answer 1

40

Explanation:

The given geometric series is:

`\sum_(n=1)^4(-2)(-3)^(n-1)`.

When n=1,
`a_1=(-2)(-3)^(1-1)`,
`\implies a_1=(-2)(-3)^(0)=-2`

When n=2,
`a_2=(-2)(-3)^(2-1)`,
`\implies a_2=(-2)(-3)^(1)=6`

When n=3,
`a_3=(-2)(-3)^(3-1)`,
`\implies a_3=(-2)(-3)^(2)=-18`

When n=4,
`a_4=(-2)(-3)^(4-1)`,
`\implies a_4=(-2)(-3)^(3)=54`

The sum of the given series is:

-2+6-18+54=40