Question

Consider the sequence:

1000,-500,250,-125
What is the 7th number in the sequence? Write your answer as a fraction

Answer 1

The 7th number in the sequence is
`(125)/(8)`

Explanation:

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio.

The nth term of a geometric sequence is given by:

`A_n = A(0)r^(n-1)`

In which A(0) is the first term and r is the common ratio.

1000,-500,250,-125

This means that
`A(0) = 1000, r = -(500)/(1000) = -(1)/(2)`

So

`A_n = A(0)r^(n-1)`

`A_n = 1000(-(1)/(2))^(n-1)`

What is the 7th number in the sequence?

This is
`A_7`. So

`A_7 = 1000(-(1)/(2))^(7-1) = (1000)/(64) = (125)/(8)`

The 7th number in the sequence is
`(125)/(8)`