Q27 of 176 Page 8

If t_n denotes the nth term of an A.P., show that t_m + t_2n+m = 2 t_m+n.

To show: t_m + t_2n+m = 2 t_m+n

Taking LHS

t_m + t_2n+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}

= 2t_m+n

= RHS

∴LHS = RHS

Hence Proved

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