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It is known that (k + 1)th term, (Tk+1), in the binomial expansion of (a + b)n is given by 
.
Therefore, (r – 1)th term in the expansion of (x + 1)n is 
r th term in the expansion of (x + 1)n is 
(r + 1)th term in the expansion of (x + 1)n is 
Therefore, the coefficients of the (r – 1)th, rth, and (r + 1)th terms in the expansion of (x + 1)n are 
respectively. Since these coefficients are in the ratio 1:3:5, we obtain
Multiplying (1) by 3 and subtracting 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 = 7 and r = 3