Question

Formulas for Sequences Practice
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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:

- \( a_1 = -5 \)
- \( a_n = a_{n-1} + 4 \)

we can calculate the next terms as follows:

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:

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