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 initial term \( a_1 = -5 \) and follow the recursive relation \( a_n = a_{n-1} + 4 \).

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

2. **Second Term**:
\[
a_2 = a_1 + 4 = -5 + 4 = -1
\]

3. **Third Term**:
\[
a_3 = a_2 + 4 = -1 + 4 = 3
\]

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