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

Answer:

448

Step-by-step 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