Question

How do you find a formula for the nth term of this arithmetic sequence: 15, 27, 39...?

Answer 1

`a_n=3+ 12n`

Explanation:

The sequence is
`15, 27, 39`

The first term:
`color(blue)(a_1=15`

The common difference of this sequence :
`color(blue)(d=27-15=12`

The `nth` term of an arithmetic sequence is given by formula
`color(blue)(a_n=a+(n-1)d`

So `a_n` for this sequence will be :
`a_n=color(blue)(15)+(n-1)color(blue)(12`
`a_n=(15)+ 12n -12`
`a_n=3+ 12n`