If an A.P. consists of n terms with first term a and n^th term l show that the sum of the m^th term from the beginning and the m^th term from the end is (a + l).

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Solution

In the given problem, we have an A.P. which consists of n terms.

Here,

The first term (a) = a

The last term (a_n) = l

Now, as we know,

So, for the m^thterm from the beginning, we take (n = m),

Similarly, for the m^th term from the end, we can take l as the first term.

So, we get,

Now, we need to prove

So, adding (1) and (2), we get,

Therefore,

Hence proved

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If an A.P. consists of n terms with first term a and nth term l show that the sum of the mth term from the beginning and the mth term from the end is (a+l).

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If an A.P. consists of n terms with first term a and nth term l show that the sum of the mth term from the beginning and the mth term from the end is (a + l).

If an A.P. consists of n terms with first term a and n^th term l show that the sum of the m^th term from the beginning and the m^th term from the end is (a + l).