Question -
Answer -
It is known that (k +1)th term, (Tk+1), in the binomialexpansion of (a + b)n is givenby 
.
Therefore, (r – 1)th termin the expansion of (x + 1)n is
r th termin the expansion of (x + 1)n is 
(r + 1)th termin the expansion of (x + 1)n is 
Therefore, the coefficients ofthe (r – 1)th, rth, and (r +1)th terms in the expansion of (x + 1)n are 
respectively. Since thesecoefficients are in the ratio 1:3:5, we obtain
Multiplying (1) by 3 andsubtracting it from (2), we obtain
4r – 12 = 0
⇒ r = 3
Putting the value of r in(1), we obtain
n –12 + 5 = 0
⇒ n = 7
Thus, n = 7and r = 3