Question

How do you find the formula for `a_n` for the arithmetic sequence `a_1=5, a_4=15`?

Answer 1

`a_n=10/3n+5/3`

Explanation:

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

`•color(white)(x)a_n=a_1+(n-1)d`

`"where d is the common difference"`

`"given "a_4=15" and "a_1=5`

`rArr5+3d=15rArrd=10/3`

`rArra_n=5+10/3(n-1)`

`color(white)(rArra_n)=5+10/3n-10/3`

`color(white)(rArra_n)=10/3n+5/3`