Question

Given the arithmetic sequence with the following two

terms, write the explicit rule.
a_5 = 25 and a_11 = 85

Answer 1

aₙ = -15 + 10 * (n-1)

Explanation:

aₙ = a₁ + (n-1)*d a₁: first term d: common difference

a₅ a₁ + 4d =25 .... (1)

a₁₁ a₁ + 10d = 85 ...(2)

(2) - (1) 6d = 60

d = 10

a₁ = -15

Formula: aₙ = -15 + 10 * (n-1)