Given the recursive formula for the arithmetic sequence a1=−5

Question

, an=an−1+4
, find the first three terms of the sequence.(2 points)

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'll calculate the terms step by step:

1. First term \( a_1 \): \[ a_1 = -5 \]

2. Second term \( a_2 \): \[ a_2 = a_1 + 4 = -5 + 4 = -1 \]

3. Third term \( a_3 \): \[ a_3 = a_2 + 4 = -1 + 4 = 3 \]

Thus, the first three terms of the sequence are:

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

So, the first three terms are \(-5, -1, 3\).