Write an

explicit formula for An, the nth

term of the sequence 22, 17, 12, ...

-5n + 27

Step-by-step 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

27 - 5n.

Step-by-step 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