Question

Following are APs or not? If they form an A.P. find the common difference d and write three more terms: 

a, 2a, 3a, 4a …

Answer 1

a, 2a, 3a, 4a …

It can be observed that

a₂ − a₁ = 2a − a = a

a₃ − a₂ = 3a − 2a = a

a₄ − a₃ = 4a − 3a = a

i.e., a_k+1 − a_k is same every time. Therefore, d = a

The given numbers are in A.P.

Three more terms are

a₅ = 4a + a = 5a

a₆ = 5a + a = 6a

a₇ = 6a + a = 7a