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Question

If in the expansion of (1 + y)n, the coefficients of 5th, 6th and 7th terms are in A.P., then n is equal to
(a) 7, 11
(b) 7, 14
(c) 8, 16
(d) none of these

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Solution

(b) 7, 14

Coefficients of the 5th, 6th and 7th terms in the given expansion are C4n , C5n and C6nThese coefficients are in AP. Thus, we have2 C5n =C4n+C6nOn dividing both sides by C5n, we get:2=C4nC5n+C6nC5n2=5n-4+n-5612n-48=30+n2-4n-5n+20n2-21n+98=0(n-14)(n-7)=0n=7 and 14

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