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Find the sum of the infinitely decreasinggp whose 3rd term, 3 times the productof the 1st and 4th term and 2nd term form an ap in the indicated orderwith common difference 1/8?

Mitanshi , 7 Years ago
Grade 11
anser 1 Answers
Vikas TU

Last Activity: 7 Years ago

Dear Student,
 terms of AP : ar^2, 3a^2r^3, ar
        Common difference = 1/8
        Hence , ar – 3a^2r^3 = 1/8 ______ (1)
                       3a^2r^3 – ar^2 = 1/8 ______ (2)
                       ar – ar^2 = 1/4 _______ (3)
(1) – (2 )  to find value of a = (1+r)/ 6r^2
Put this value in (3) to get r=1/2
Sum of GP = a/(1-r) = 2.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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