Question

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

Answer 1

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

1. The first term is given as:
\[
a_1 = -5
\]

2. To find the second term \( a_2 \):
\[
a_2 = a_1 + 4 = -5 + 4 = -1
\]

3. To find the third term \( a_3 \):
\[
a_3 = a_2 + 4 = -1 + 4 = 3
\]

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

The final answer is:
- \( a_1 = -5 \)
- \( a_2 = -1 \)
- \( a_3 = 3 \)