Given the recursive formula for the arithmetic sequence a1=−5 , an=an−1+4 , find the first three terms of the sequence.(2 points)

Question

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 each term step by step:

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

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

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

So, the first three terms of the sequence are:

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

Putting it all together:

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