Question

Which of the following sequence is not an A.P.?

Options

• `2, 5/2, 3, 7/2, ...`

• –1.2, –3.2, –5.2, –7.2, ...

• `sqrt(2), sqrt(8), sqrt(18), ...`

• 1², 3², 5², 7², ...

Answer 1

1², 3², 5², 7², ...

Explanation:

(A) `2, 5/2, 3, 7/2, ...`

`5/2 - 2 = 0.5`

`3 - 5/2 = 0.5`

Difference is constant (d = 0.5). This is an A.P.

(B) –1.2, –3.2, –5.2, –7.2, ...

–3.2 – (–1.2) = –2

–5.2 – (–3.2) = –2

Difference is constant (d = –2). This is an A.P.

(C) `sqrt(2), sqrt(8), sqrt(18), ...`

Simplify the terms: `sqrt(2), 2sqrt(2), 3sqrt(2), ...`

`2sqrt(2) - sqrt(2) = sqrt(2)`

`3sqrt(2) - 2sqrt(2) = sqrt(2)`

Difference is constant `(d = sqrt(2))`. This is an A.P.

(D) 1², 3², 5², 7², ...

Calculate the values: 1, 9, 25, 49, ...

9 – 1 = 8

25 – 9 = 16

The difference is not constant. This is not an A.P.