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)
a1= ___, a2= ___, and a3=___

Answer 1

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

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:

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

So, the final answers are: \( a_1 = -5 \), \( a_2 = -1 \), and \( a_3 = 3 \).