Question

Consider the sequence 1,2,3,4,5...

What is the recursive formula that represents the sequence for the term numbers 1,2,3,4
, and 5
?

Responses

Answer 1

To represent the sequence 1, 2, 3, 4, 5, ..., we can create a recursive formula where each term depends on the previous term. The sequence can be defined as follows:

- **Base case**: \( a(1) = 1 \)
- **Recursive case**: \( a(n) = a(n-1) + 1 \) for \( n > 1 \)

This means that the first term of the sequence is 1, and each subsequent term is obtained by adding 1 to the previous term.

So, the recursive formula for the sequence is:
- \( a(1) = 1 \)
- \( a(n) = a(n-1) + 1 \) for \( n \geq 2 \)