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प्रश्न
Which of the following is NOT a geometric progression?
विकल्प
`1/3, 1, 3, 9`
`1/5, 1/5, 1/5, 1/5`
–2, 4, –8, 16
2, 0, 4, 0, 8, 0
MCQ
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उत्तर
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.
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