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.

1²,2², 3², 4²,...

Answer 1

a₂ – a₁

= 2² – (1)²

= 4 – 1

= 3

a₃ – a₂

= 3² – (2)²

= 9 – 4

= 5

a₄ – a₃

= 4² – (3)²

= 16 – 9

= 7

i.e., a_{k + 1} – a_k is not the same every time.