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 Problems 63-66, write the first five terms of each sequence.
64. a1 = 3 and an = 2an-1 -2for n≥ 2
66. a1=1 and an = - 1/3an_1 for n ≥ 2