Question

Write an
explicit formula for an, the nth term of the sequence 112, 28, 7, ....

Answer 1

It's a geometric sequence

• r=112/28=1/4

Test with third term to verify

• 28(1/4)=7

Verified

Now

find formula

`\\ \tt\hookrightarrow a_n=ar^(n-1)`

`\\ \tt\hookrightarrow a_n=112(1/4)^(n-1)`

Answer 2

`a_n=112 \cdot \left(\frac14 \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 = 112 \implies a=112`

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

`\implies r=(a_3)/(a_2)=(7)/(28)=\frac14`

Therefore,
`a_n=112 \cdot \left(\frac14 \right)^(n-1)`