Complete the recursive formula of the arithmetic sequence

Question

.-3, -1,1,3,….
b(1) = ____
b(n) = b(n - 1) + ___

Answer 1

To complete the recursive formula of the arithmetic sequence -3, -1, 1, 3,…, let's identify the first term and the common difference.

1. The first term \( b(1) \) is the first term in the sequence: \[ b(1) = -3 \]

2. Next, we find the common difference by subtracting the first term from the second term: \[ \text{Common difference} = -1 - (-3) = -1 + 3 = 2 \]

So, the formula can be completed as follows:

• The first term is \( b(1) = -3 \).
• The recursive formula is \( b(n) = b(n - 1) + 2 \).

Therefore, the completed answers are: \[ b(1) = -3 \] \[ b(n) = b(n - 1) + 2 \]