Question

Write an explicit formula for an, the nth term of the sequence 36, 32, 28, ....
WORTH 20

Answer 1

an = 36 + -4(n - 1)

Explanation:

Explicit formula:

`a_n=a_1+(n-1)d`

Where:

• an = nth term
• a1 = first term
• d = common difference

Here, we are given the following:

• Sequence: 36, 32, 28

The first term is 36

To get to the next term, 4 is subtracted from the previous term so the common difference is -4.

So we have:

• First term(a1) = 36
• Common difference = -4

By plugging this into
`a_n=a_1+(n-1)d`

We acquire :
`a_n=36+(n-1)(-4)`