Question

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.
$$
\begin{aligned}
&a_{18}-a_{14}=32 \\
&\Rightarrow(a+17 d)-(a+13 d)=32 \\
&{\left[a_{n}=a+(n-1) d\right]} \\
&\Rightarrow 4 d=32 \\
&\Rightarrow d=8
\end{aligned}
$$
Thus, the common difference of the AP is 8 .

Answer 2

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Answer 3

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