What is the value of 10 - 8 + 6 - 4 + ... - (-20) ?
8
10
12
14
16
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Integer Properties
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Look for a PATTERN.
Sum of the first 2 terms = 10 - 8 = 2.
Sum of the first 4 terms = (sum of the first 2 terms) + 6 - 4 = 4.
Sum of the first 6 terms = (sum of the first 4 terms) + 2 - 0 = 6.
Note the pattern exhibited by the values in red.
If n is EVEN, then the sum of the first n terms = n.
From 10 to -20 there are a total of 16 even integers.
The sum of the first 16 terms of the sequence = 16.
The correct answer is E.
On the GMAT, a formula for the sequence would be given.
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We could also determine the sum of every successive PAIR of terms:
10 - 8 = 2.
6 - 4 = 2.
2 - 0 = 2.
-2 - (-4) = 2.
-6 - (-8) = 2.
-10 - (-12) = 2.
-14 - (-16) = 2.
-18 - (-20) = 2.
Since there a total of 8 pairs, and the sum of each pair is 2, the sum of the entire set = 8*2 = 16.
The correct answer is E.
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This is the set of 16 even integers with 8 positive and other 8 negative integersWhat is the value of 10 - 8 + 6 - 4 + ... - (-20) ?
8
10
12
14
16
First alternate integer series
10+6+2-2-6-10-14-18 = -32 (Sum of last two terms because rest cancel out)
Second alternate integer series
-8-4-0+4+8+12+16+20 = 28+20 (Sum of last three terms because rest cancel out)
Sum of them all = -32+28+20 = [spoiler]16 Answer Option E[/spoiler]
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Wow, three answers and nobody used the method I did ... couldn't resist joining in![email protected] wrote:What is the value of 10 - 8 + 6 - 4 + ... - (-20) ?
Notice that the first eleven terms of our sum just cancel out (I've written this so it's clear, but you don't need to do this on test day, as you know the series will alternate pos/neg):
10 - 8 + 6 - 4 + 2 - 0 + (-2) - (-4) + (-6) - (-8) + (-10)
So we really have 10 - 10 -8 + 8 + 6 - 6 etc. or a sum of 0.
Hence we only have to sum the last four terms:
12 - 14 + 16 - 18 + 20, or
-2 + -2 + 20, or 16
