Q. 27

If tn denotes the nth term of an A.P., show that tm + t2n+m = 2 tm+n.

Answer :

To show: tm + t2n+m = 2 tm+n


Taking LHS


tm + t2n+m = a + (m – 1)d + a + (2n + m – 1)d


= 2a + md – d + 2nd + md – d


= 2a + 2md + 2nd – 2d


= 2 {a + (m + n – 1)d}


= 2tm+n


= RHS


LHS = RHS


Hence Proved


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