Question

The following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms.

3, 3, 5, 5,....

Answer 1

a₂ − a₁

= 3 − 3

= 0

a₃ − a₂

= 5 − 3

= 2

a₄ − a₃

= 5 − 5

= 0

The consecutive differences are 0, 2, 0, not all equal. Therefore, the list 3, 3, 5, 5, ... does not form an A.P. and there is no common difference d to give, so you cannot write the “next three terms” as terms of an A.P.