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, 0, −3, −6,...

Answer 1

a₂ − a₁

= 0 − 3

= −3

a₃ − a₂

= −3 − 0

= −3

a₄ − a₃

= −6 − (−3)

= −3

All consecutive differences are equal (−3), so the sequence is an A.P. with common difference d = −3.

Find the next three terms by adding d each time:

a₅ = a₄ + d

= −6 + (−3)

= −9

a₆ = a₅ + d

= −9 + (−3)

= −12

a₇ = a₆ + d

= −12 + (−3)

= −15

It is an A.P., d = −3, next three terms −9, −12, −15.