Question

What is a formula for the nth term of the given sequence?5, -25, 125...

Answer 1

Given the sequence below:

`5,-25,125,\ldots`

It can be observed that the sequence shown is a geometric sequence.

The nth term of a geometrical sequence is given by the formula below:

`a_n=ar^(n-1)`
`\begin{gathered} \text{where } \\ a_n=\text{nth term} \\ a=\text{first term} \\ r=\text{common ratio} \end{gathered}`

From the given sequence, we can determine a, and r as shown below

`\begin{gathered} a=5 \\ r=(a_2)/(a_1)=(-25)/(5)=-5 \end{gathered}`

Substitute for a and r in the formula to get the nth term as shown below

`a_n=5(-5)^(n-1)`
`a_n=5(-(1)/(5))^(1-n)`

Hence, the nth term is, as shown above