Question

The third term in a sequence is 11.

The term-to-term rule is "take away 4".
Write an expression, in terms of n, for the nth term of the sequence.​

Answer 1

a(n) = a(n - 1) - 4, with a(1) = 19

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

Answer 2

23 - 4n

Explanation:

3rd term is 11, so the 2nd term is 15, and the first term is 19.

19 takeaway 4 is 15

15 takeaway 4 is 11

The expression is term[n] = 23 - 4n

Thank you