<p>A sequence of numbers begins with the numbers -1,1,1,...,
and each term afterward is the product of the proceeding three terms.
How many of the first 57 terms of this sequence are negative?</p>
<p>1)19
2)20
3)28
4)29
5)30</p>
<p>Here from this logic we can see that this is combined of 4 groups.</p>
<p>so 57/4 we removed the remainder and got 14 * 4 = 56;</p>
<p>But now the question is how can I calculate the negatives fast,so if I see this kind of problems in SAT I solve it really fast :).</p>
<p>Thanks.</p>
<p>GenericMath,
I’m not sure what you mean by your question. The way I would solve this problem is to write out terms until I see a pattern. </p>
<p>-1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1 . . . . </p>
<p>There is a four-term pattern of -1, 1, 1, -1 (I think this is what you meant by combined of 4 groups). In each four-term pattern, two terms are negative. </p>
<p>4 goes into 57 fourteen times with one left over, so we have fourteen full patterns, which gives us 28 negative numbers. The one left over will be negative, since the first term of the pattern is negative. </p>
<p>I hope this helps.</p>
<p>^Yes Thanks it helped I just didn’t understand how to get the count of the negative,but makes sense to me now.</p>
<p>Thanks.</p>
<p>-1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1</p>
<p>once you notice that pattern from the fourth term onward all you have to do is get rid of the first three terms for now. So now you have 57-3 = 54 terms. You noticed in the pattern that there are two negative terms for two positive terms. That means that half are negative, 54/2 = 27. But wait you have to go back to the first three terms and you see there is one more negative 1. Add that and you get 27+1 = 28. Pretty much the same thing as above.</p>
<p>^Nice Explanation too 
thanks alot.</p>