Sequence And Series Question 276

Question: If $ a,\ b,\ c $ , d are any four consecutive coefficients of any expanded binomial, then $ \frac{a+b}{a},\ \frac{b+c}{b},\ \frac{c+d}{c} $ are in

Options:

A) A.P.

B) G.P.

C) H.P.

D) None of the above

Show Answer

Answer:

Correct Answer: C

Solution:

Let $ a={}^{n}{C_{r-1}},\ b={}^{n}C_{r},,C={}^{n}{c_{r+1}} $ and $ d={}^{n}{c_{r+2}} $ . Substituting these values in problem, we get $ \frac{a+b}{a},\ \frac{b+c}{b},\ \frac{c+d}{c} $ are in H.P.