Question

How do you find the formula for `a_n` for the arithmetic sequence `a_1=x, d=2x`?

Answer 1

`a_n=(2n-1)x`

Explanation:

`n^(th)` term `a_n` of an arithmetic sequence, whose first term is `a_1` and common difference is `d` is given by

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

Here `a_1=x` and `d=2x`, therefore `a_n` is given by

`a_n=x+(n-1)2x=x+(2n-2)x=(1+2n-2)x=(2n-1)x`