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

Question

Philoid · Accepted Answer

Here, second term = a₂ = 14

Third term = a₃ = 18

∴ Common difference = a₃ - a₂ = 18 - 14 = 4

Thus first term = a = a₂ - d = 14 - 4 = 10

Now, Sum of first n terms of an AP is given by

S_n = [2a + (n - 1)d]

∴ Sum of first 51 terms is given by:

S₅₁ = [2(10) + (51 - 1)(4)]

= (51/2) × [20 + 200]

= (51/2) × 220

= (51) × 110

= 5610

∴ S₅₁ = 5610