Question

What is the fifteenth term of the sequence 5,-10,20,-40,80?

Answer 1

`a_15=81920`

Explanation:

from the given set of numbers 5,-10,20,-40,80...it appears like Geometric Sequence and with first term `a_1=5` and the common ratio `r=80/(-40)=(-40)/20=20/(-10)=(-10)/5=-2`

`r=-2`

the formula to find the `nth` term in Geometric Progression is

`a_n=a_1*r^(n-1)`

Use now `a_1=5` and `r=-2` and `n=15` in the formula

`a_n=a_1*r^(n-1)`

`a_15=5*(-2)^(15-1)`

`a_15=5*(-2)^(14)`

`a_15=5*16384`

`a_15=81920" " "`the 15th term

A long check helps after all there are only 15 numbers

5, -10, 20, -40, 80, -160, 320, -640, 1280, -2560, 5120, -10240, 20480, -40960, 81920

God bless....I hope the explanation is useful...