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CGP EDU Academic Team
Published on: August 14, 2026
The sum of three numbers which are consecutive terms of an A.P. is 21. If the second number is reduced by 1 & the third is increased by 1, we obtain three consecutive terms of a G.P., find the numbers.
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3, 7, 11 or 12, 7, 2
Sol. Let a – d , a, a + d ⇒ 3a = 21 ⇒ a =7
a – d, a –1, a + d + 1 are in G.P ⇒ 7 – d, 6 , 8 + d are in G.P
⇒ 36 = (7– d) (8 + d) ⇒ 36 = 56 – d –d 2
⇒ d 2 + d – 20 = 0 ⇒ d = –5 , 4
so Numbers are 3, 7, 11 ⇒ 12, 7, 2
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