Q. 27

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

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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