Question

How do you find the formula for `a_n` for the arithmetic sequence `a_1=1, d=3`?

Answer 1

`a_n=3n-2`

Explanation:

a generalised AP is given by

`a,a+d,a+2d,....a+(n-1)d`

in this case we have

`a_1=1,d=3`

so

`a_n=1+3(n-1)=1+3n-3`

`a_n=3n-2`

Answer 2

`a_n=3n-2`

Explanation:

`"the nth term of an arithmetic sequence is "`

`•color(white)(x)a_n=a+(n-1)d`

`"where a is the first term and d the common difference"`

`"here "a=1" and "d=3`

`rArra_n=1+3(n-1)=3n-2`