Question

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

 0, -4, -8, -12, …

Answer 1

0, −4, −8, −12 …

It can be observed that

a₂ − a₁ = (−4) − 0 = −4

a₃ − a₂ = (−8) − (−4) = −4

a₄ − a₃ = (−12) − (−8) = −4

i.e., a_k+1 − a_k is same every time. Therefore, d = −4

The given numbers are in A.P.

Three more terms are

a₅ = − 12 − 4 = −16

a₆ = − 16 − 4 = −20

a₇ = − 20 − 4 = −24