Answer:
a(n) = a(n - 1) - 4, with a(1) = 19
Step-by-step explanation:
If the rule for finding each new term is "take away 4," then this is an arithmetic sequence with first term a(1) (unknown) and third term 11. The "common difference" is -4.
Then the formula for this arithmetic sequence is found as follows:
The third term is 11. The previous (second) term is 4 greater, or 15. The first term (coming before 15) is 19.
Thus, the general formula is
a(n) = a(n - 1) - 4, with a(1) = 19
Check: Does a(1) come out to 19? Is 19 - 4(1 - 1) = 19? YES
Does a(2) come out to 15? Is 19 - 4 = 15? YES
Does a(3) come out to 11? Is 15 - 4 = 11? YES
