Which one of the following is not an A.P.?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3, 9, 19, 33, 51
An arithmetic progression (A.P.) is a list in which every term is obtained by adding the same number, the common difference, to the term before it. So a list is an A.P. only if the differences of consecutive terms are all equal.
Option (1) 11, 7, 3, −1, −5 — differences \(-4,-4,-4,-4\): an A.P.
Option (2) 0, −3, −6, −9 — differences \(-3,-3,-3\): an A.P.
Option (3) 3, 9, 19, 33, 51 — differences 6, 10, 14, 18: not equal, so this is not an A.P. (the differences themselves grow by 4)
Option (4) 9, 13, 17, 21, 25 — differences 4, 4, 4, 4: an A.P.