Question

In an A.P., the 4th and 6th terms are 6 and 14, respectively. Find the sum of its 20 terms.

Answer 1

a₆ − a₄ = (a + 5d) − (a + 3d) = 2d

14 − 6 = 2d

8 = 2d

d = 4

The value of d into the equation for the 4th term:

a + 3d = 6

a + 3(4) = 6

a + 12 = 6

a = 6 − 12

= −6

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

`S_20 = 20/2[2(-6) + (20 - 1)4]`

S₂₀ = 10[(-12) + 19 × 4]

S₂₀ = 10[-12 + 76]

S₂₀ = 10 × 64

S₂₀ = 640

The sum of the first 20 terms of the A.P. is 640