Question

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

Answer 1

Answer:

Given

a2 = 14

a3 = 18

n = 51

The common difference

d = a3 - a2 = 18 - 14 = 4

d = 4

a2 = a + d = 14

==> a + 4 = 14

==> a = 14 - 4

==> a = 10

Now , Sum of 51 terms

S^n = n [ ( 2a + ( 50 ) d ] /2

===> 51 [ ( 2 × 10 ) + 50 × 4 ] / 2

===> 51 [ 20 + 200 ] / 2

===> 51 [ 220 ] / 2

===> 51 × 110

===> 5610

Sum of 51 terms is 5610 .