Question

Two terms of an arithmetic sequence are a7 = 32 and a19 =140. Find a rule for the nth term.

Answer 1

Answer:

aₙ = 9n - 31

Step-by-step explanation:

If we call the common difference as d, since 19 - 7 = 12, we can write:

32 + 12d = 140

12d = 108

d = 9 which means that a₁ = a₇ - 6d = 32 - 6 * 9 = -22.

Explicit formula for arithmetic sequence: aₙ = a₁ + (n-1)d so the answer is

aₙ = -22 + (n - 1) * 9

= -22 + 9n - 9

= 9n - 31