Let a,b and c be in G.P. with common ratio r where a≠0 and 0

Let a,b and c be in G.P. with common ratio r where a0 and 0<r1/2. If 3a, 7b and  15c are the first three terms of an A.P., then the 4th term of this A.P. is:

  1. A

    7a/3

  2. B

    a

  3. C

    5a

  4. D

    2a/3

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    Solution:

    Given, a, band  c  are in G.P. with common ratio r.

     b=ar and  c=ar2  ……………… …(i)

    Also, 3a,7b and 15c are in A.P.            [Given]

        3a+15c=14b 

    3a+15ar2=14ar          [Using (i)] 

    15r214r+3=015r29r5r+3=0(3r1)(5r3)=0

    r=1/3  or 3/5r=1/3            [r(0,1/2]]

        The required A.P. is  3a,7a/3,5a/3,

    Hence, 4th term is 3a/3 = a

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