Question

Write an
explicit formula for An, the nth
term of the sequence 22, 17, 12, ....

Answer 1

27 - 5n.

Explanation:

This is arithmetic with common difference = 17 - 22 = -5 (also 12 - 17 = -1).

nth term an = a1 + d(n - 1)

= 22 - 5(n - 1)

Which simplifies to 27 - 5n

Answer 2

-5n + 27

Explanation:

The difference is -5.

The first term is 22.

Use the formula for nth term.

an = dn + (a - d)

a is the first term.

d is the difference.

an = - 5n + (22 - ( - 5 ))

an = -5n + (22 + 5)

an = -5n + 27