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The Sum of first N consecutive odd integers is N^2. What is

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The Sum of first N consecutive odd integers is N^2. What is [#permalink] New post 02 Aug 2006, 16:34
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The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 39 inclusive.

A. 351
B. 364
C. 410
D. 424
E. 450
[Reveal] Spoiler: OA
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 [#permalink] New post 02 Aug 2006, 16:40
B....


1- 11 are the first 6 odd intergers; sum = 6^2 = 36

1- 39 are the first 20 odd intergers; sum = 400

sum of odd nos frm 13- 39 = 400-36 = 364
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 [#permalink] New post 02 Aug 2006, 18:44
Use AP and you woudn't need the supplied formula:

a(1) = 13; a(n) = a(1) + (n-1)d = 39 (where d =2).
Sum = n/2[a(1) + a(n)] = 364, where n = 14
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 [#permalink] New post 02 Aug 2006, 22:24
Number of odd numbers from 1-39 = 39+1/2 = 20
Sum = 400

Number of odd numbers between = 1-12 = (12 - 1 +1)/2 = 6
sum = 36

Sum between 13-39 inclusive = 400 - 36 = 364
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 [#permalink] New post 03 Aug 2006, 08:03
I also used AP without using N^2 condition. For me, sometimes, it is easeir to just stick to basics and do the calcs. This way, at least, I know I will arrive at the correct answer sooner or later...
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 [#permalink] New post 03 Aug 2006, 23:41
I would suggest using the formula, for the simple reason that instead of an AP the problem might refer to some fancy formula for an unknown sequence of numbers.

Anyway here we go...

For odd integers till 39, number of integers = 20
Sum = 20^2 = 400
For odd integers till (but not including 13), number of integers = 6
Sum = 6^2 = 36
Difference = 364 = B
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Re: PS : Number Prop. [#permalink] New post 04 Aug 2006, 05:43
ghantark wrote:
The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 39 inclusive.

351
364
410
424
450

OA later


i never knew this formulea that sum of n consecutive odd integers = n^2.
however, we can use regular formula:
the sum of consecutive odd integers from 13-39 = n (L-s)/2 = [{(39-13)/2} +1][39-13] = 14 x 26 = 364
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Re: PS : Number Prop. [#permalink] New post 05 Aug 2006, 00:03
Professor wrote:
ghantark wrote:
The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 39 inclusive.

351
364
410
424
450

OA later


i never knew this formulea that sum of n consecutive odd integers = n^2.
however, we can use regular formula:
the sum of consecutive odd integers from 13-39 = n (L-s)/2 = [{(39-13)/2} +1][39-13] = 14 x 26 = 364


It can be derived from the regular formula for A.P.

1+3+5+....=n/2[2.1+(n-1).2] = n^^2 !!
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Re: PS : Number Prop. [#permalink] New post 05 Aug 2006, 14:37
ghantark wrote:
The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 39 inclusive.

351
364
410
424
450

OA later


Sum of odd integers from 1 to 39 inclusive = 20^2=400
sum of odd integers from 1 to 11 inclusive = 6^2 = 36
therfore sum of odd integers between 13 and 39 incl = 400 -36 = 364

Hence B

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Re: The Sum of first N consecutive odd integers is N^2. What is [#permalink] New post 07 Jun 2012, 00:58
I method -
the sum of odd numbers till 39(inclusive) =n^2=20^2

the sum of odd numbers till 11 (inclusive) =n^2=6^2

20^2 -6^2=(20-6)(20+6)=26*14=364

================

II method
n* (a1+an)/2
n=((39-13)/2)+1=14

(39+13)/2* 14=26*14=364
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Re: The Sum of first N consecutive odd integers is N^2. What is   [#permalink] 07 Jun 2012, 00:58
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