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?

The answer should be 10, but I'm not sure how to get there.

Find the pattern. When you increase n by 1 you decrease the number by 3. So if Tsub1 is 23 then Tsub2 is 20 and Tsub3 is 17...so you see that between 23 and -4 is a total of 27. So that means divide 27 by 3 and you get 9. But you already started with Tsub1 so that is 9 plus the one you started with or tsub10.

Hey Nelly,

Almost always, the best way to solve sequence problems is to write out a couple terms to get a feel for the pattern. If T1 is 23, and T2 = T1 - 3, then T2 = 20, and we have:

T1 = 23
T2 = 20
T3 = 20 - 3 = 17
T4 = 17 - 3 = 14

Then we can just keep subtracting threes until we get to -4:

T5 = 11
T6 = 8
T7 = 5
T8 = 2
T9 = -1
T10 = -4

You could theoretically get more algebraic with this, but for most sequence problems it's sufficient to jot out a few terms, get a feel for the pattern, and then finish it off as far as necessary.