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

Question

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

(1 point)
Responses

an=1; an=an−1+an+1
an=1; an=an−1+an+1

an=1; an=an−1+an−1
an=1; an=an−1+an−1

an=1; an=an−1+2
an=1; an=an−1+2

an=1; an=an−1+1

Answer 1

To represent the sequence 1, 2, 3, 4, 5, ... recursively, we need to specify the first term and a relationship for subsequent terms.

1. The first term \( a_1 \) is 1.
2. Each subsequent term can be defined as \( a_n = a_{n-1} + 1 \).

Thus, the correct recursive formula is:

• \( a_1 = 1 \)
• \( a_n = a_{n-1} + 1 \) for \( n > 1 \)

From the options provided, the correct response is:

an=1; an=an−1+1.