Question

If the n^th term of a progression be a linear expression in n, then prove that this progression is an AP

Answer 1

Let the n^th term of a given progression be given by T_n = an + b, where a and b are constants.

Then, T_n-1 = a(n – 1) + b = [(an + b) – a]

∴ (T_n – T_n-1 ) = (an + b) – [(an + b) – a] = a,

which is a constant.

Hence, the given progression is an AP