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# What is the average of the first 15 positive integers?

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Joined: 02 Sep 2009
Posts: 52431
What is the average of the first 15 positive integers?  [#permalink]

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28 Feb 2018, 23:40
00:00

Difficulty:

25% (medium)

Question Stats:

85% (00:32) correct 15% (00:25) wrong based on 36 sessions

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What is the average of the first 15 positive integers?

(A) 7

(B) 7.5

(C) 8

(D) 8.5

(E) 9

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What is the average of the first 15 positive integers?  [#permalink]

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01 Mar 2018, 00:04
Bunuel wrote:
What is the average of the first 15 positive integers?

(A) 7

(B) 7.5

(C) 8

(D) 8.5

(E) 9

Here, we are talking about an AP with an odd number of elements.
In such a set,
1. the middle term is the average of the AP.
2. the average is the average of first and last elements in the AP.

Since it is a small set, we can write it down to clarity: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15

Average is 8(the middle term) or $$\frac{1+15}{2} = \frac{16}{2} = 8$$

Therefore, the average of the first 15 positive integers is 8(Option C)
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Re: What is the average of the first 15 positive integers?  [#permalink]

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01 Mar 2018, 01:50
Bunuel wrote:
What is the average of the first 15 positive integers?

(A) 7

(B) 7.5

(C) 8

(D) 8.5

(E) 9

this question can be solved in several ways. we have to find the sum of all the positive integers
which can be done by using this formula:

n(n+1)/2
=15*16/2
=120
average =120/15
=8
option c is the correct one.
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Re: What is the average of the first 15 positive integers?  [#permalink]

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02 Mar 2018, 09:39
Bunuel wrote:
What is the average of the first 15 positive integers?

(A) 7

(B) 7.5

(C) 8

(D) 8.5

(E) 9

Since we have a set of consecutive integers, we can determine the average using the following equation:

average = (1st integer + last integer)/2

average = (1 + 15)/2 = 16/2 = 8

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What is the average of the first 15 positive integers?  [#permalink]

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03 Mar 2018, 02:36
Bunuel wrote:
What is the average of the first 15 positive integers?

(A) 7

(B) 7.5

(C) 8

(D) 8.5

(E) 9

IMO C
sum of 1st 15 positive integer
=n*(a+l)/2 (n=no. of terms, a= first term , and l is last term)
=15(1+15)/2
=15*8
average = 15*8/15=8
What is the average of the first 15 positive integers? &nbs [#permalink] 03 Mar 2018, 02:36
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