Some sequences are defined by a recursion formula —that is, a formula that defines each term of the sequence in terms of one or more of the preceding terms. For example, if {an} is defined by
a1 = 1 and an = 2an−1 + 1 for n ≥ 2
then
a2 = 2a1 + 1 = 2 • 1 + 1 = 3
a3 = 2a2 + 1 = 2 • 3 + 1 = 7
a4 = 2a3 + 1 = 2 • 7 + 1 = 15
and so on. In Problem write the first five terms of the sequence.
a1 = 2 and an = 3an−1 + 2 for n ≥ 2
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