Question -
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.