Question

The 8th term of an arithmetic sequence is 12 and its 12th term is 8. What is the algebraic expression for this sequence?

Answer 1

Difference between terms = 8 – 12 = -4

To get the 12th term from the 8td term, we must add the common difference (9 – 5 = 4) 4 times.

Common difference = – 4 / 4 = -1

Algebraic expression for arithmetic series

x_n = an + b

12 = – 1 × 8 + b ⇒ 12 = – 8 + b

b = 12 + 8 = 20

Algebraic expression for arithmetic series = xn = –1 × n + 20 = 20 – n