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What is the sum of the first 100 positive odd numbers?

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New post 25 Nov 2016, 02:26
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What is the sum of the first 100 positive odd numbers?

A. 5,000 B. 7,500 C. 8,000 D. 10,000 E. 12,000

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What is the sum of the first 100 positive odd numbers?  [#permalink]

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New post 25 Nov 2016, 02:48
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This one is about pattern recognition. Set up a table as follows:

Number Sum
1 1
3 4
5 9
7 16
9 25

Now as you see, the sum always equals the perfect square of the number of odd integers that you want to sum. So the sum of the first 5 odd integers is 5^2 = 25. The pattern continues. Thus, the sum of the first 100 odd integers will be equal to 100^2 = 10,000. The correct answer is (D).
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Re: What is the sum of the first 100 positive odd numbers?  [#permalink]

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New post 25 Nov 2016, 03:44
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For first n odd numbers, its n^2 and for first n even numbers, its n (n+1)

Here, it'll be (100)^2 = 10000

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Re: What is the sum of the first 100 positive odd numbers?  [#permalink]

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New post 25 Nov 2016, 06:01
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MathRevolution wrote:
What is the sum of the first 100 positive odd numbers?

A. 5,000 B. 7,500 C. 8,000 D. 10,000 E. 12,000


Before answering any GMAT quant problem, always check the answer choices first
Here, the answer choices are somewhat spread apart, which means we can be somewhat aggressive in our estimations.

Nice formula: 1 + 2 + 3 . . . + n = (n)(n + 1)/2

Let's use the above formula to find the sum of the first 200 integers (including odds AND evens)
1 + 2 + 3 . . . + 199 + 200 = (200)(200 + 1)/2
= (200)(201)/2
= (100)(201)
= 20,100
So, the sum of the first 200 integers is 20,100
HALF of those integers are ODD and HALF are even. So, this sum includes the sum of the first 100 ODD integers and the sum of the first 100 EVEN integers.
So, the sum of the first 100 ODD integers is APPROXIMATELY 20,100/2
20,100/2 = 10,050
So, the sum of the first 100 ODD integers ≈ 10,050
Answer choice D is the only one that's close to 10,050 so it must be the correct answer.

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New post 28 Nov 2016, 01:41
==> Since 1+3+5+….+(2n-1)=n 2, 1+3+…….(2*100-1)=100 2 =10,000 is derived.

Hence, the answer is D.
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New post 14 Dec 2016, 07:57
The sum of an arithmetic sequence equals (n(first term) + n(last term)/2)*n.

N1 = 1.
N 100 = N0 + (n-1)*2 = 1 + 198 = 199.

Now sum = ((1+199)/2)*100 = 100*100 = 10,000.
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Re: What is the sum of the first 100 positive odd numbers?  [#permalink]

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New post 20 Jan 2017, 23:52
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MathRevolution wrote:
What is the sum of the first 100 positive odd numbers?

A. 5,000 B. 7,500 C. 8,000 D. 10,000 E. 12,000


Sum of first n positive odd numbers = \(n^2\)

Therefore, Sum of first 100 positive odd numbers = \(100^2\) = 10000;

Hence option D is correct.
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Re: What is the sum of the first 100 positive odd numbers?   [#permalink] 19 Jul 2018, 21:56
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