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Sequence S consists of 24 nonzero integers. If each term in [#permalink]

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13 Nov 2006, 13:56

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Sequence S consists of 24 nonzero integers. If each term in S after the second is the product of the previous two terms, how many terms in S are negative?

Sequence S consists of 24 nonzero integers. If each term in S after the second is the product of the previous two terms, how many terms in S are negative?

n1, n2, (n1*n2)=> positive, well if n1 and n2 are both negative then we have 1 number of negative elements..if n1 and n2 are both postive then we have 0 elements which are negative...INSUFF

2) fourth term is negative

n1, n2, [n1*n2], [n1*n2^2], this implies that n1 is negative..we dont know if n2 is negative or not..if it is..then we have a number of negative elements if not then we have another sufficient...

Combining them is sufficient..both n1 and n2 are negative...and we know exactly how many negative elements there are...

Is there are an easy way to find there are 16 - term in both the cases?
-,-,+,-.... and
-,+,-,- cases?
Or did you wrote down all the 24 terms and counted?

Is there are an easy way to find there are 16 - term in both the cases? -,-,+,-.... and -,+,-,- cases? Or did you wrote down all the 24 terms and counted?

Since it has a pattern, 2 -ves and 1+ve, I think we need not list everything, and can go with 2/3 of 24 for -ve. Not sure if there is any other way.

Hi Sumitra,
yes, there is a pattern -,-,+. But the first elements are differnt
--+
-+-
If you consider only 8 elements, in the first case, there are 6 -ivs, and 2 +ive.
In the 2nd sequence, there are 5-ivs and 3 +ivs.

So how do you know that 24 elements will have the same no. of negatives.[/quote]

Hi Sumitra, yes, there is a pattern -,-,+. But the first elements are differnt --+ -+- If you consider only 8 elements, in the first case, there are 6 -ivs, and 2 +ive. In the 2nd sequence, there are 5-ivs and 3 +ivs.

So how do you know that 24 elements will have the same no. of negatives.

[/quote]

Hi,
It is the same three --+/-+- that follows. Every three numbers should have 2 -ves and 1+ve, so out of 24, 16 -ves and 8 +ves.

However, I would say, when we know that it is gonna be the same --+/-+-
it would not take too long to list out the signs than to derive a shorter route.