Question

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

Answer 1

To find the first three terms of the arithmetic sequence defined by the recursive formula, we start with the given values.

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

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

3. To find the third term (\(a_3\)), we again use the recursion formula:
\[
a_3 = a_2 + 4 = -1 + 4 = 3
\]

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

Therefore, the first three terms of the sequence are \(-5, -1, 3\).