Class 10 Math All topics Arithmetic Progressions

What is the common difference of an A.P. in which $a_{18}−a_{14}=32$?

(a)

8

(b)

-8

(c)

-4

(d)

4

Correct answer: (a)

Solution:

We know that

$a_{n}=a+(n−1)d$

Given

$a_{18}−a_{14}=32$

$⇒[a+(18−1)d]−[a+(14−1)d]=32$

$⇒a+17d−a−13d =32$

$⇒4d=32$

$⇒d=432 =8$

Hence, the common difference is $8$

And the correct answer is option $[A]$

Similar topics

introduction to trigonometry

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