Express the sequence given below as a recursively-defined function.
A.
u(0) = 3
u(n + 1) = u(n) + 8
for n = 0, 1, 2, ...
B.
u(0) = 3
u(n + 1) = 2u(n) + 5
for n = 0, 1, 2, ...
C.
u(0) = 3
u(n + 1) = 8u(n) + 1
for n = 0, 1, 2, ...
D.
u(0) = 3
u(n + 1) = 3u(n) + 2
for n = 0, 1, 2, ...
A. The recursively-defined function for this sequence is u(n) = 3 + 8n, for n = 0, 1, 2, ...
B. The recursively-defined function for this sequence is u(n) = 3(2^n) - 2, for n = 0, 1, 2, ...
C. The recursively-defined function for this sequence is u(n) = 3(8^n) - 1, for n = 0, 1, 2, ...
D. The recursively-defined function for this sequence is u(n) = 3(3^n) - 2, for n = 0, 1, 2, ...
A. The recursively-defined function for sequence A is:
u(0) = 3
u(n + 1) = u(n) + 8
B. The recursively-defined function for sequence B is:
u(0) = 3
u(n + 1) = 2u(n) + 5
C. The recursively-defined function for sequence C is:
u(0) = 3
u(n + 1) = 8u(n) + 1
D. The recursively-defined function for sequence D is:
u(0) = 3
u(n + 1) = 3u(n) + 2
A. The sequence in question starts with 3 and each subsequent term is obtained by adding 8 to the previous term. To express it as a recursively-defined function, we can use the following formula:
u(0) = 3
u(n + 1) = u(n) + 8
B. Similar to sequence A, the sequence starts with 3 and each term is obtained by doubling the previous term and adding 5. The recursively-defined function for this sequence is:
u(0) = 3
u(n + 1) = 2u(n) + 5
C. In this sequence, the initial term is 3 and each subsequent term is obtained by multiplying the previous term by 8 and adding 1. The recursively-defined function for this sequence is:
u(0) = 3
u(n + 1) = 8u(n) + 1
D. Similarly, the sequence starts with 3, and each term is obtained by multiplying the previous term by 3 and adding 2. The recursively-defined function for this sequence is:
u(0) = 3
u(n + 1) = 3u(n) + 2