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

Examine the succession of differences, decision that this is an arithmetic succession, future the rule:

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

Write out the primary succession:

##10, 18, 26, 34##

Write out the succession of differences of that succession:

##8, 8, 8##

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

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

The frequented formula for ##a_n## is:

##a_n = 8n+2##

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