Question

If in the expansion of (1 + y)ⁿ, the coefficients of 5^th,6^th and 7^th terms are in A.P., then n is equal to :

A. 7, 11 

B. 7, 14 

C. 8, 16 

D. None of these

Answer 1

Option : (B)

Given :

(1 + y)ⁿ

Since,

T₅, T₆ & T₇ are in AP 

Then; 

2(T₆) = T₅ + T₇

⇒ 30+(n-4) (n-5)-12(n-4)=0 

⇒ 30+n²-9n+20-12n+48=0 

⇒ n² - 21n + 98 = 0 

⇒ (n-7) (n-14) = 0 

⇒ n = 7,14