(6(1) - -7

b(n) - b(n - 1) + 12
Find the 4'" term in the sequence.

1 answer

To find the 4th term in the sequence defined by the recurrence relation \( b(n) = b(n - 1) + 12 \), we first need to establish the first term of the sequence.

Let's assume \( b(1) = 6(1) - -7 \).

Calculating \( b(1) \): \[ b(1) = 6(1) + 7 = 6 + 7 = 13 \]

Now we proceed to calculate the subsequent terms using the recurrence relation \( b(n) = b(n - 1) + 12 \):

  1. Finding b(2): \[ b(2) = b(1) + 12 = 13 + 12 = 25 \]

  2. Finding b(3): \[ b(3) = b(2) + 12 = 25 + 12 = 37 \]

  3. Finding b(4): \[ b(4) = b(3) + 12 = 37 + 12 = 49 \]

So, the 4th term \( b(4) \) is: \[ \boxed{49} \]