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Question -

In an A.P., show that am+n + amтАУn = 2am.



Answer -

We know the first termis тАШaтАЩ and the common difference of an A.P is d.

Given:

am+n +amтАУn = 2am

By using the formula,

an = a+ (n тАУ 1)d

Now, let us take LHS:am+n + am-n

am+n +am-n = a + (m + n тАУ 1)d + a + (m тАУ n тАУ 1)d

= a + md + nd тАУ d + a+ md тАУ nd тАУ d

= 2a + 2md тАУ 2d

= 2(a + md тАУ d)

= 2[a + d(m тАУ 1)] {тИ╡ an = a + (n тАУ 1)d}

am+n +am-n = 2am

Hence Proved.

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