Question

Question 2
In an arithmetic progression, the 8th term is twice the 3rd term and the 20th term is 110.
a) Find the common difference.

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Answer 1

a₈ = 2*a₃

a₂₀ = 110

d - ?

a_n = a₁ + (n-1)*d,

a₈ = a₁ + 7d,

a₃ = a₁ + 2d

a₂₀ = a₁ + 19d,

a₁ + 7d = 2*(a₁ + 2d),

a₁ + 7d = 2a₁ + 4d,

7d - 4d = 2a₁ - a₁

a₁ = 3d,

a₁ + 19d = 110,

3d + 19d = 110,

22d = 110,

d = 110/22 = (11*2*5)/22 = 5.

Ответ. d=5.