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# The sum of all consecutive odd integers from −21 to 31, inclusive, is

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The sum of all consecutive odd integers from −21 to 31, inclusive, is  [#permalink]

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27 Jun 2015, 03:32
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Difficulty:

25% (medium)

Question Stats:

77% (01:29) correct 23% (02:07) wrong based on 163 sessions

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The sum of all consecutive odd integers from −21 to 31, inclusive, is

A. 130
B. 135
C. 150
D. 156
E. 235

The sum of odd integers from -21 to 21 is zero because each negative value cancels out its positive counterpart. Based on this, add odd integers from 22 to 31 to get the sum of consecutive integers from -21 to 31.

23 + 25 + 27 + 29 + 31 = 135.

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Re: The sum of all consecutive odd integers from −21 to 31, inclusive, is  [#permalink]

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27 Jun 2015, 03:55
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reto wrote:
The sum of all consecutive odd integers from −21 to 31, inclusive, is

A. 130
B. 135
C. 150
D. 156
E. 235

The sum of odd integers from -21 to 21 = - 21 - 19 - 17 ---------+17 + 19 + 21 + 23 + 25 + 27 + 29 + 31

The sum of odd integers from -21 to 21 = 0 + 5* 27 = 0 + 135 = 135

When the terms are separated by a constant amount then Mean = media = Average of first and last term

Sum of 23 + 25 + 27 + 29 + 31 = 27(mean) * 5(no. of terms) = 135

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##### General Discussion
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Joined: 28 Dec 2015
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Re: The sum of all consecutive odd integers from −21 to 31, inclusive, is  [#permalink]

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30 Jun 2016, 22:06
-21 to +21=sum=0
Now add the rest of them
23+25+27+29+31=135
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Re: The sum of all consecutive odd integers from −21 to 31, inclusive, is  [#permalink]

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19 Aug 2017, 05:14
By using the formulas of AP Last term = First Term + (Number of terms - 1 ) X Difference, 31 = -21 + (n-1) X 2 ==> we get Number of terms = 27.
and by Sum of AP = n/2 X (First term + last term ), S = 27/2 X (-21+31) ==> we get Sum = 135.
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Re: The sum of all consecutive odd integers from −21 to 31, inclusive, is  [#permalink]

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19 Aug 2017, 06:18
The answer is B. From -21 to +21 is zero. Then, 23+25+27+29+31=135.

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Re: The sum of all consecutive odd integers from −21 to 31, inclusive, is   [#permalink] 19 Aug 2017, 06:18
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