Question

Write an explicit formula for a,, the nth term of the sequence 72, -12, 2, ....

Answer 1

`a_n=72 \cdot \left(-\frac16 \right)^(n-1)`

Explanation:

The difference between each term in the sequence is not the same, therefore the sequence is a geometric sequence.

Geometric sequence formula:
`a_n=a r^(n-1)`

where
`a` is the start term and
`r` is the common ratio

Given
`a_1 = 72 \implies a=72`

To calculate
`r`, divide one term by its previous term:

`\implies r=(a_3)/(a_2)=(2)/(-12)=-\frac16`

Therefore,
`a_n=72 \cdot \left(-\frac16 \right)^(n-1)`