Another Dumb Sat Question

Discus: SAT/ACT Tests and Test Preparation: June 2004 Archive: Another Dumb Sat Question
 By Ericlu87 (Ericlu87) on Tuesday, June 22, 2004 - 01:38 am: Edit

1, 2, 1, -1, -2,...

The first five terms of a sequence are shown above. After the second term, each term can be obtained by subtracting from the previous term the term before that. For example, the third term can be obtained by subtracting the first term from the second term. What is the sum of the first 36 terms of the sequence?

(A)0
(B)4
(C)12
(D)24
(E)30

The answer is A and i dont know why im stupid sorry.

 By Loop123 (Loop123) on Tuesday, June 22, 2004 - 01:55 am: Edit

The first twelve terms of the sequence look like this.

1,2,1,-1,-2,-1,
1,2,1,-1,-2,-1...

Notice that the sum of each of the sets of six terms is 0. Thus, the sum of the thirty-six terms in the sequence are 6 * 0 = 0, so the answer is A.

 By Loop123 (Loop123) on Tuesday, June 22, 2004 - 01:55 am: Edit

The first twelve terms of the sequence look like this.

1,2,1,-1,-2,-1,
1,2,1,-1,-2,-1...

Notice that the sum of each of the sets of six terms is 0. Thus, the sum of the thirty-six terms in the sequence is 6 * 0 = 0, so the answer is A.

P.S. You are NOT stupid. Everyone as strengths and weaknesses. The stupid thing to do would have been to dismiss the problem entirely.

 By Apemanttt (Apemanttt) on Tuesday, June 22, 2004 - 01:56 am: Edit

1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1....

Now look how this sequences repeats: 1, 2, 1, -1, -2, -1,

The sum of that sequence is 0

That sequences occurs 36/6 = 6 times (six because there are six numbers in the repeated sequences and 36 in the whole). You don't even need to figure out how many times the numbers are repeated if you know the sequence adds up to 0 though.

So anyways, we have 0 x 6 = 0 or more simply 0 because of what I said in the preceding paragraph.

 By Haithman (Haithman) on Tuesday, June 22, 2004 - 02:07 am: Edit

Ok so we know the first 5 terms are 1,2,1,-1,and -2. To find the sixth term, subtract the fourth term (which is -1), from the fifth term (which is -2). -2-(-1)= -1. Now we find the seventh term by subtracting the fifth from the sixth, or -2-(-1) which equals 1. If we do this once more to find the eigth term, we do the seventh term (1) minus the sixth term (-1), and we get 2.
From here, we can see that there is a pattern...the numbers repeat every sixth term.
So for the first 36 terms of the sequence, it consists of 36/6 or 6 groups of numbers with the given pattern (1,2,1,-1,-2,-1). So to find the sum of the first 36 terms, find the sum of the first six terms and multiply by 6. So 1+2+1+-1+-2+-1=0. 0x6=0. The sum of the first 36 terms is 0 therefore (A.) is correct.
Hope that helped!

 By Haithman (Haithman) on Tuesday, June 22, 2004 - 02:07 am: Edit

Damn sorry im late, its 2 and took me awhile to write that...I need sleep...

 By Ericlu87 (Ericlu87) on Tuesday, June 22, 2004 - 06:21 pm: Edit

haha crap i was doing -6 -7 -8 etc...damn me