Given the recursive formula for the arithmetic sequence a1=15, an=an−1+22 . Find the third term in the sequence.(1 point) Responses a3=59 A sub 3 is equal to 59 a3=37 A sub 3 is equal to 37 a3=−7

Answer 1

To find the third term \( a_3 \) of the arithmetic sequence defined by the recursive formula \( a_n = a_{n-1} + 22 \) with the initial term \( a_1 = 15 \), we can calculate each term step by step.

1. The first term is given as: \[ a_1 = 15 \]

2. To find the second term \( a_2 \): \[ a_2 = a_1 + 22 = 15 + 22 = 37 \]

3. Now to find the third term \( a_3 \): \[ a_3 = a_2 + 22 = 37 + 22 = 59 \]

Thus, the third term in the sequence is \( a_3 = 59 \).

The correct response is: \[ a_3 = 59 \]