Question

The sum of the 8th element and the 12th element of an arithmetic progression

is 246. The sum of the 10th and the 14th element is 298. What is the value of
the 35th term?

Answer 1

448

Explanation:

aₙ = a₁ + (n-1)d

a₈ = a₁ + (8-1)d = a₁ + 7d

a₁₂ = a₁ + 11d

a₈ + a₁₂ = 246 = 2a₁ + 18d a₁ + 9d = 123

a₁₀ + a₁₄ = a₁ + 9d + a₁ + 13d = 298 a₁ + 11d = 149

2d = 26

d = 13

a₁ = 6

a₃₅ = 6 + (35-1) x 13 = 448