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

To Find: S₅₁

Given: a₂ = 14, a₃ = 18


We have; a₂ = 14, a₃ = 18 and n = 51

We know,

d = a₃ – a₂ = 18 – 14 = 4

Therefore, d = 4

a₂ – a = 4

14 – a = 4

a = 10

So, first term = 10

Now, sum can be calculated as follows:

Where, a and d are first term and common difference respectively.

= 51 x (20 + 200)/2

= 51 x 110

= 5610

S₅₁ = 5610