Question

The sum of the first 12 terms of an A.P. is 900. If its first term is 20, then find the common difference and 12^th term.

Answer 1

Given, a = 20, and the sum of 12 and the term is 900.

Using the formulas for the sum of n terms of an A.P.

S_n = `n/2 [2a + (n − 1) d]`

S₁₂ = `12/2 [2 xx 20 + (12 − 1) d]`

900 = 6 [40 + 11d]

900 = 240 + 66d

66d = 900 − 240

66d = 660

d = `660/66`

∴ d = 10

Using the formula for the n^th term to find a₁₂.

a_n = a + (n − 1) d

a₁₂ = 20 + (12 − 1) × 10

= 20 + 110

= 130