Let a , b , c be in G.P. with ratio r , where a  = 0 and 0 < r ≤ 1/2 . If 3 a , 7 b , 15 c are the first three terms of an A.P., its fourth term is:

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MathematicsSequence & SeriesMiscellaneous/MixedMedium2 minQB

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Let $a, b, c$ be in G.P. with ratio $r$ , where $a \neq = 0$ and $0 < r \leq 1/2$ . If $3 a, 7 b, 15 c$ are the first three terms of an A.P., its fourth term is:

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Answer:

Solution:

$14 a r = 3 a + 15 a r^{2}$ , so $(3 r - 1) (5 r - 3) = 0$ . The allowed ratio is $r = 1/3$ . The A.P. difference is $7 a /3 - 3 a = - 2 a /3$ . Its fourth term is $3 a + 3 (- 2 a /3) = a$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Miscellaneous/Mixed

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