QJEEM19Mab321: JEE Main 2019 Mathematics - Class 11 JEEM19Mab321 Solution: Let , b and c be in G.P. with common ratio r, where 0 and 0 < r …

Question

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Let

a

, b and c be in G.P. with common ratio r, where

a

\ne

0 and 0 < r

\le

{1 \over 2}

. If 3

a

, 7b and 15c are the first three terms of an A.P., then the 4^th term of this A.P. is :

Accepted Answer

a = a, b = ar and c = ar²

3a, 7b, 15c

\to

A.P.

14b = 3a + 15c

14(ar) = 3a + 15(ar²)

15r² – 14r + 3 = 0

\Rightarrow r = {1 \over 3},{3 \over 5}(rejected)

Common difference = 7b – 3a

= 7ar – 3a

\Rightarrow

{{7a} \over 3} - 3a = - {2 \over 3}a

4^th term is

\Rightarrow

15c - {2 \over 3}a = {{15} \over 9}a - {2 \over 3}a = a

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