If the coefficients of three consecutive terms in the expansion of 1 + x n are in the ratio 1 : 7 : 42 , then the value of n is equal to

Question

If the coefficients of three consecutive terms in the expansion of 1 + x n are in the ratio 1 : 7 : 42 , then the value of n is equal to, 49, 50, 55, 56

MARKS App · Accepted Answer

For T r + 1 = n C r x r , coefficient → n C r n C r - 1 : n C r : n C r + 1 = 1 : 7 : 42 ⇒ n C r n C r - 1 = 7 1 and n C r + 1 n C r = 42 7 ⇒ n - r + 1 r = 7 and n - r r + 1 = 6 ⇒ n - r + 1 = 7 r and n - r = 6 r + 6 ⇒ n = 8 r - 1 and n = 7 r + 6 ⇒ 8 r - 1 = 7 r + 6 ⇒ r = 7 ⇒ n = 55

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