Question

Which of the following is the general term for the sequence m, -m, m, -m, . . .?

Answer 1

The answer on odyssey is m(-1)^n-1

Answer 2

nth term formula is
`a_n=m(-1)^(n-1)`

Explanation:

the sequence m, -m, m, -m, . .

The difference between the terms is 0 . so lets find the common ratio

To find common ratio , divide the next term by previous term

`(m)/(-m) =-1`

`(-m)/(m) =-1`

Common ratio -1. It is a geometric sequence

General term for the sequence is

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

where a1 is the first term and 'r' is the common ratio

a1=m , r=-1

`a_n=m(-1)^(n-1)`