What is the common difference

Question:

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

(a) 8

(b) $-8$

(c) $-4$

(d) 4

Solution:

(a) Given, $a_{18}-a_{14}=32$

$\Rightarrow \quad a+(18-1) d-[a+(14-1) d]=32$

$\left[\because a_{n}=a+(n-1) d\right]$

$\Rightarrow \quad a+17 d-a-13 d=32$

$\Rightarrow \quad 4 d=32$

$\therefore \quad d=8$

which is the required common difference of an AP.

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