In the arithmetic sequence t1, t2, t3....tn t1 = 23 and tn=tn-1 - 3 for each n>1.
What is the value of n when tn = -4

A) -1
B) 7 *
C) 10
D) 14
E) 20

One of many approaches:

We know that each term is 3 less than the previous term. We also know that the "distance" between the first term 23 and the term -4 is -4 - 23 = -27. So, that tells us that the term -4 is -27/-3 = 9 terms away from the first term. So the answer is 10.

Another approach is simply to list out the pertinent terms of the sequence:

23, 20, 17, 14, 11, 8, 5, 2, -1, -4. Here it's really clear that n is 10 when tn is -4.

Rey