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QUESTION

# What is the recursive rule for the sequence 10, 18, 26, 34....?

Examine the sequence of differences, finding that this is an arithmetic sequence, hence the rule:

a_1 = 10 a_(n+1) = a_n + 8

Write out the original sequence:

10, 18, 26, 34

Write out the sequence of differences of that sequence:

8, 8, 8

So this is an arithmetic sequence, definable by the rule:

a_1 = 10 a_(n+1) = a_n + 8

The direct formula for a_n is:

a_n = 8n+2