Question

Prove that no matter what is the real number a and b are, the sequence with nth term a+nb is always an A.P. What is the common difference?

Answer 1

No matter what is the real number a and b, sequence with nth term a+nb is always an AP.

• Let nth term Tn=a+nb.
• Since the nth term depends linearly on n, we conclude that sequence is an Arithmetic Progression (AP).
• The common difference (d) = nth term - (n+1)th term = (a+nb) - (a+(n-1)b) = b

Hence, common difference = b.