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, we start with the provided values:

1. **First Term:**
\( a_1 = -5 \)

2. **Second Term:**
Using the recursive formula \( a_n = a_{n-1} + 4 \):
\[
a_2 = a_1 + 4 = -5 + 4 = -1
\]

3. **Third Term:**
Again using the recursive formula:
\[
a_3 = a_2 + 4 = -1 + 4 = 3
\]

Putting this all together:
- \( a_1 = -5 \)
- \( a_2 = -1 \)
- \( a_3 = 3 \)

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