Question

Write a recursive rule for the sequnce 6, 10, 14, 18, 22, ...

Answer 1

This is an example of a arithmetic sequence because the common difference is the same through the set of numbers;

14 - 10 = 4

18 - 14 = 4

22 - 18 = 4

Common Difference is 4.

Recursive Rule: an = a1 + (n - 1)d

an = nth term

a1 = first term

n = number of the term

d = common difference

We know that;

a1 = 10

n = placement of the number

d = 4

Put into the rule:

an = 10 + (n - 1)4

Best of Luck!