Question

Given the recursive formula for the arithmetic sequence a1=−5 , an=an−1+4 , find the first three terms of the sequence.(2 points) a1= , a2= , and a3=

Answer 1

To find the first three terms of the arithmetic sequence given the recursive formula \( a_1 = -5 \) and \( a_n = a_{n-1} + 4 \), we can compute the terms step by step.

1. **First term**:
\[
a_1 = -5
\]

2. **Second term**:
\[
a_2 = a_{1} + 4 = -5 + 4 = -1
\]

3. **Third term**:
\[
a_3 = a_{2} + 4 = -1 + 4 = 3
\]

So the first three terms of the sequence are:
- \( a_1 = -5 \)
- \( a_2 = -1 \)
- \( a_3 = 3 \)