Question

What sequence does A(n+1) = A(n) - 3 for n >= 1 and A(1) = 5 generate?

Answer 1

The sequence generated by A(n+1) = A(n) - 3, starting with A(1) = 5, is an arithmetic sequence with each term 3 less than the previous term, resulting in a pattern that decreases linearly by 3.

Step-by-step explanation:

The sequence generated by A(n+1) = A(n) - 3 for n ≥ 1 and A(1) = 5 is an arithmetic sequence where each term is 3 less than the previous term. Starting with A(1) = 5, we can calculate a few terms of the sequence to understand its pattern:

• A(2) = A(1) - 3 = 5 - 3 = 2
• A(3) = A(2) - 3 = 2 - 3 = -1
• A(4) = A(3) - 3 = -1 - 3 = -4

Thus, the sequence continues by subtracting 3 from the previous term, resulting in a linear pattern of numbers that decreases by 3 with each step in the sequence. This sequence is called an arithmetic sequence or arithmetic progression.