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

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Answer 1 · 2015-10-30T08:45:55

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#