Question

Choose the correct answer in each of the following questions:

What is the common difference of an AP in which $a_{18}-a_{14}=32$?

(a) 8 (b) −8 (c) 4 (d) −4

Answer 1

Let a be the first term and d be the common difference of the AP. Then,

$$\begin{gathered} a_{18}-a_{14}=32 \\ \Rightarrow \left(a+17d\right)-\left(a+13d\right)=32\left[a_n=a+\left(n-1\right)d\right] \\ \Rightarrow 4d=32 \\ \Rightarrow d=8 \end{gathered}$$

Thus, the common difference of the AP is 8.

Hence, the correct answer is option is A.