SAT Math problem help

[In The Great White North]

Good morning! Can any of the math gurus help with this problem? When I saw it, I immediately started with the first number and added/multiplied my way up to 55 (well, eventually, I saw a pattern) and did get the right answer. After watching Dana Mosely, ds says their should be a formula and that the SAT doesn't design them to have to be figured out the way I did it (takes too long?). It's from the big blue practice book, test #1. What's the formula?

3, 5, -5,...

The first term in the sequence of numbers shown above is 3. Each even-numbered term is 2 more than the previous term and each odd numbered term is -1 times the previous term. For example, the second term is 3 + 2, and the third term is (-1) x 5. What is the 55th term of the sequence?



a) -5
b) -3
c) -1
d) 3
e) 5


TIA

[MyThreeSons]

The idea is to recognize the pattern and then determine what the particular term would be. In this case, I would see that there is a set of four terms that appear in sequence, and then repeat: 3, 5, -5, -3. 56 is a multiple of 4, so the 56th term would be -3; the 55th term would be the one before that, or -5.

Your son is right in that you don't want to write out the whole sequence to 55. They could just have easily asked for the 1000th term .... But there isn't a nice formula like F(n) = .....

HTH

[Sharon in MD]

There are 4 terms in a complete sequence. so divide 55 by 4 and you get 13 complete sequences. Multiply 13 x 4 and you get 52, which where the last -3 will land. Therefore, the 55th term will be -5.

Is that right?

[LoriM]

There are 4 terms in a complete sequence. so divide 55 by 4 and you get 13 complete sequences. Multiply 13 x 4 and you get 52, which where the last -3 will land. Therefore, the 55th term will be -5.

Is that right?

Yes, it's pretty much the same way you figure out powers of the complex number i (sqrt (-1)). If you want to find out what i ^55 is, I always teach my students to use the chart:

i = i
i^2 = -1
i^3 = -i
i^4 = 1

So you take 55 mod 4 (which is just divide by 4, and get the remainder). Divide by 4 (you don't even care that it's 13...that's extra info!), and your remainder is 3. So i^55 = i^3 = -i

[Sharon in MD]

Ah yess! of course....the only thing that matters in this case is using the remainder to figure out where you are in the sequence. ;)