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There is an finite number of elements in a sequence. What is [#permalink]

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26 Nov 2005, 07:38

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13. There is an finite number of elements in a sequence. What is the sum of all the elements in that sequence?

(1) There are negative numbers to correspond with all positive numbers in that sequence with the same absolute value.
(2) The number of positive and negative elements is the same.
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Last edited by gamjatang on 01 Dec 2005, 00:28, edited 1 time in total.

"there are negative numbers to correspond with all positive numbers" doesnt mean that all neg. numbers correspond with all pos n unless the number of elements is the same
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"there are negative numbers to correspond with all positive numbers" doesnt mean that all neg. numbers correspond with all pos n unless the number of elements is the same

Wow.. you're right ..
we just tend to assume that it is the same case other way round as well that for every negative no there is a positive no

Both (1) and (2) are sufficient. sum of n-terms in the sequence= middle value * n.
1) is insufficient. if n-number of terms is even, average is 0, then n+(n-1)+(n-2).....+=0. e.g. -5; -3; -1; 1; 3; 5 However, if n-odd, e.g -5; -3; -1; 1; 3; 5; 7=1. Middle number can have any value depending on the sequence, if n is odd.

2) also insufficient, middle value can'be found from the information given.

Cobining both statements will suffice, since n is even and -ve and +ve numbers correspond, n+(n-1)+(n-2)....=0
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(1)baiscally says that for all positive numbers there is an equal and positive negative number, however we dont know that for every negative number there is an equal positive number...insuff

(2) is also insufficient, there are equal number of negative numbers and given that we dont know the exact value of the numbers...

together, we still dont know the exact values of the negative numbers
say for example...

sequence is
-3, -2, -1, 2, 1, 1, so as you can see we have a repeat of positive number and we have an equal value negative number....the sum is -2....

sequence can also be
-3, -2, 2, 3...in this case the sum is 0...

(1)baiscally says that for all positive numbers there is an equal and positive negative number, however we dont know that for every negative number there is an equal positive number...insuff

(2) is also insufficient, there are equal number of negative numbers and given that we dont know the exact value of the numbers...

together, we still dont know the exact values of the negative numbers say for example...

sequence is -3, -2, -1, 2, 1, 1, so as you can see we have a repeat of positive number and we have an equal value negative number....the sum is -2....

sequence can also be -3, -2, 2, 3...in this case the sum is 0...

Well, yeah. But -3, -2, -1, 2, 1, 1 is not an algebraic sequence because the difference between the terms is not always the same. Am I right?
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Hmmm I believe that a sequence is basically a set where the order of elements is defined. In other words a, b, c is a different sequence of a, c, b. However a sequence doesn't have to have a certain formula for you to be able to derive each element. It doesn't even need to be monotonically increasing or decreasing, I believe.

In other words, -3, -2, -1, 2, 1, 1 can be a sequence, in my opinion.
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