Question

How do I find the `n`th term of an arithmetic sequence?

Answer 1

`a_n=a_1+(n-1)*d`
`color(white)("XXX")`where `a_1` is the first term and
`color(white)("XXXXXXX")d` is the difference between a term and its previous term.

Explanation:

Examine the pattern:

`a_1`
`a_color(brown)(2)=a_1+d=color(green)(a_1+1d)`
`a_color(brown)(3)=a_2+d=a_1+d+d=color(green)(a_1+2d)`
`a_color(brown)(4)=a_3+d=a_1+2d+dcolor(green)(=a_1+3d)`
`a_color(brown)(5)=a_4+d=a_1+3d+d=color(green)(a_1+4d)`