The integer sequence a1, a2, a3, . . ., defined explicitly by the formula an = 5n for n e Z+, can also be defined recursively by
1) a1 = 5; and
2) an+1, an + 5, for n > 1.
For the integer sequence b1, b2, b3, . . . , where bn = n(n + 2) for all n ∈ Z+, we can also provide the recursive definition:
1) b1 = 3; and
2) bn+1 = bn + 2n + 3, for n > 1.
Give a recursive definition for each of the following integer sequences c1, c2, c3, . . ., where for all n ∈ Z+ we have
a) cn = 7n
b) cn = 7n
c) cn = 3n + 7
d) cn = 7
e) cn = n2
f) cn = 2 - (-1)n