Question

For any AP, the expression for the $n^{th}$ term is always a ___ expression in $n$.

Answer 1

We know that $n^{th}$ term of an AP is given by a + (n-1)d where a = first term, d = common difference, $a_n$ = $n^{th}$ term.
Rearranging further a + (n-1)d we get,
$a_n=dn+(a-d)$ which is a linear expression in ‘n’. ('a’ and ‘d’ are constants, and the highest power on the variable n is 1)