Question

The first, second and the last terms of an A.P are a, b, c respectively prove that the sum is ((a + c)(b + c - 2a))/(2(b - a))

Answer 1

1st term is a, common difference = d = b – a.

Let ‘n’ be the number of term in the series.

∴ c = a + (n – 1)d

⇒ (n – 1)d = c – a

⇒ (n – 1 )(b – a) = c – a

⇒ n – 1 = (c - a)/(b - a)

⇒ n = (c - a)/(b - a) + 1

= n/2{2a + c – a} = n/2{a + c}

= ((b + c - 2a)/(b - a))((a + c)/2)