Question

What is the next term of the geometric sequence?-2.5, 5, -10, 20,...

Answer 1

EXPLANATION

A geometric sequence has a constant ratio r and it's defined by:

`a_n=a_0\cdot r^(n-1)`

Check wheter the ratio is constant:

-2.5, 5, -10, 20,...​

Compute the ratio of all the adjacent terms:

`r=(a_(n+1))/(a_n)`

5/-2.5= -2 , -10/5 = -2, 20/-10=-2

The ratio of all the adjacent terms is the same and equal to:

r= -2

The first element of this sequence is:

`a_1=-2.5`
`a_n=a_1\cdot r^(n-1)`

So, the next term of the sequence is:

`a_5=-2.5\cdot-2^(5-1)`

Simplifying:

`a_5=-2.5\cdot16`

So, the next term is a_5 = -40