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# 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##