Given the recursive formula for the arithmetic sequence a1=15, an=an−1+22

Question

. Find the third term in the sequence.(1 point)
Responses

a3=37
A sub 3 is equal to 37

a3=−7
A sub 3 is equal to negative 7

a3=59
A sub 3 is equal to 59

Answer 1

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

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

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

3. To find the third term: \[ a_3 = a_2 + 22 = 37 + 22 = 59 \]

Thus, the third term \( a_3 \) is: \[ a_3 = 59 \]

Therefore, the answer is: a3=59