(Q27).Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Given A.P in which

a2 = a +     d = .....(1)

a3 = a + d = ......(2)

- d = -

Substituting d = in equation (1),

we get, a + =

⇒ a = – =

Now, Sn =
n
2
 [a+l]
=
n
2
 [2a + (n - 1)d]
S51 =
2
 [2 × + ( - 1) × ]
=
2
 [ + × ]
=
2
 ( + )
=
2
 × = × =