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Question

In an arithmetic progression the sum of two terms equidistant from the beginning and the end is always _____ to the sum of the first and last terms.

A
equal
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B
unequal
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C
different
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D
various
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Solution

The correct option is A equal
Let a be first term d be common difference of an AP having n number of terms.
So mth term from the beginning is, am=a+(m1)d
and m the term from end is anm=a+(n1)d(m1)d=a+(nm)d
So am+anm=2a+(n1)d=[a]+[a+(n1)d]= sum of first and last term

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