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 defined by the recursive formula \( a_1 = -5 \) and \( a_n = a_{n-1} + 4 \), we can calculate 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:**
\[
a_3 = a_2 + 4 = -1 + 4 = 3
\]

Therefore, the first three terms of the sequence are:

- \( a_1 = -5 \)
- \( a_2 = -1 \)
- \( a_3 = 3 \)

So, the final answers are:
\( a_1 = -5 \), \( a_2 = -1 \), and \( a_3 = 3 \).