To find the fourth term in the sequence defined by the given recurrence relation, we first need to establish the base case and then use the recurrence relation to calculate the subsequent terms.
We are given:
- \( b(1) = -7 \)
- The recurrence relation: \( b(n) = b(n - 1) + 12 \)
Now we can calculate the consecutive terms:
-
First term:
\( b(1) = -7 \) -
Second term:
\( b(2) = b(1) + 12 = -7 + 12 = 5 \) -
Third term:
\( b(3) = b(2) + 12 = 5 + 12 = 17 \) -
Fourth term:
\( b(4) = b(3) + 12 = 17 + 12 = 29 \)
Thus, the fourth term in the sequence is \( b(4) = 29 \).