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 given the recursive formula, we start with the provided values:

1. First Term:
   \( a_1 = -5 \)

2. Second Term:
   Using the recursive formula \( a_n = a_{n-1} + 4 \): \[ a_2 = a_1 + 4 = -5 + 4 = -1 \]

3. Third Term:
   Again using the recursive formula: \[ a_3 = a_2 + 4 = -1 + 4 = 3 \]

Putting this all together:

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

Thus, the first three terms of the sequence are:

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