Question

Which of the following is NOT a geometric progression?

Options

• `1/3, 1, 3, 9`

• `1/5, 1/5, 1/5, 1/5`

• –2, 4, –8, 16

• 2, 0, 4, 0, 8, 0

Answer 1

2, 0, 4, 0, 8, 0

Explanation:

A G.P. requires a constant common ratio r = `"Term"/"Previous term"`.

(a) Ratios: `1 ÷ 1/3 = 3`

3 ÷ 1 = 3

9 ÷ 3 = 3

⇒ r = 3 (GP)

(b) Ratios: Each term divided by the previous = 1

⇒ r = 1 (GP)

(c) Ratios: 4 ÷ (–2) = –2 

(–8) ÷ 4 = –2 

16 ÷ (–8) = –2 

⇒ r = –2 (GP)

(d) 0 ÷ 2 = 0 but 4 ÷ 0 is undefined.

So, no single constant r exists.

Therefore, 2, 0, 4, 0, 8, 0 is not a GP.