Given the recursive formula for the geometric sequence: a1=4, an=3an−1−7 , find the second term of the sequence.(1 point)

Answer 1

To find the second term of the geometric sequence defined by the recursive formula \( a_1 = 4 \) and \( a_n = 3a_{n-1} - 7 \), we can compute \( a_2 \):

1. Start with the first term: \[ a_1 = 4 \]

2. Use the recursive formula to find the second term: \[ a_2 = 3a_1 - 7 \]

3. Substitute \( a_1 \) into the formula: \[ a_2 = 3(4) - 7 \]

4. Calculate the value: \[ a_2 = 12 - 7 = 5 \]

Thus, the second term of the sequence is \( a_2 = 5 \).