Question

Evaluate the geometric series. Please help me out!!!

Answer 1

- 1364

Explanation:

The n th term of a geometric series is

`a_(n)` = a
`(r)^(n-1)`

where a is the first term and r the common ratio

4
`(-2)^(n-1)` ← is an n th term

with a = 4 and r = - 2

The sum to n terms of a geometric series is

`S_(n)` =
`(a(r^(n)-1) )/(r-1)`, thus

`S_(10)` =
`(4((-2)^(10)-1) )/(-2-1)`

=
`(4(1024-1))/(-2-1)`

=
`(4(1023))/(-3)`

=
`(4092)/(-3)`

= - 1364