The integer sequence a1, a2, a3, . . . , defined explicitly by the formula an  5n for n ∈ 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

cn = 7n (c sub n = 7 sub n).

Please show steps. I have no idea where to start with this.

Question

The integer sequence a1, a2, a3, . . . , defined explicitly by the formula an  5n for n ∈ 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

cn  = 7n  (c sub n = 7 sub n).

Please show steps.  I have no idea where to start with this.

anonymous · Answer

c_1 = 7
c_(n+1) = c_n + 7 for n>=1