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Question

If a1, a2, a3, ....., an, ..... is an A.P. such that a18 – a14 = 32, then its common difference is __________.

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Solution

Given:
a18 – a14 = 32

Now,
an=a+n-1da18=a+18-1d=a+17da14=a+14-1d=a+13d a18-a14=a+17d-a+13d32=17d-13d32=4dd=8

Hence, if a1, a2, a3, ....., an, ..... is an A.P. such that a18 – a14 = 32, then its common difference is 8.

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