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The sum of seven consecutive integers is equal to 7. What is the avera

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The sum of seven consecutive integers is equal to 7. What is the avera [#permalink]

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New post 05 Nov 2017, 03:07
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The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the sequence?

(A) 7

(B) 4

(C) 2

(D) 1

(E) -2
[Reveal] Spoiler: OA

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Re: The sum of seven consecutive integers is equal to 7. What is the avera [#permalink]

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New post 05 Nov 2017, 03:16
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Here, Seven consecutive number is -2, -1, 0, 1 , 2, 3, 4
So, Average of highest and least number is 1

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Re: The sum of seven consecutive integers is equal to 7. What is the avera [#permalink]

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New post 05 Nov 2017, 04:12
Bunuel wrote:
The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the sequence?

(A) 7

(B) 4

(C) 2

(D) 1

(E) -2


As its an AP.. a-3d + a-2d+a-d+a+a+d+a+2d+a+3d = 7
a=1

a-3d+a+3d/2= 1

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Re: The sum of seven consecutive integers is equal to 7. What is the avera [#permalink]

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New post 05 Nov 2017, 06:29
Bunuel wrote:
The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the sequence?

(A) 7

(B) 4

(C) 2

(D) 1

(E) -2


Let the 7 consecutive integers be a-3d , a-2d , a-d , a , a+d , a+2d and a+3d
Sum = 7a = 7
=> a = 1
Least term = a-3d = 1-3 = -2
Greatest term = a+3d = 1+3 = 4
Average = (-2+4)/2 = 1

Answer D
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Re: The sum of seven consecutive integers is equal to 7. What is the avera [#permalink]

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New post 05 Nov 2017, 06:47
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Let the first term be x

Sum of seven consecutive numbers = 7x+21
Now 7x+21=7

x=-2

Hence average of first & last term is (-2+4)/2=1

Option D
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The sum of seven consecutive integers is equal to 7. What is the avera [#permalink]

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New post 05 Nov 2017, 10:25
Bunuel wrote:
The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the sequence?

(A) 7

(B) 4

(C) 2

(D) 1

(E) -2


7 sum/7 integers=1 average
D

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Re: The sum of seven consecutive integers is equal to 7. What is the avera [#permalink]

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New post 12 Nov 2017, 08:49
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Expert's post
Bunuel wrote:
The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the sequence?

(A) 7

(B) 4

(C) 2

(D) 1

(E) -2


Since 7 consecutive integers sum to 7, we can let x = the first integer and create the following equation:

x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 = 7

7x + 21 = 7

7x = -14

x = -2

Thus, the first integer is -2 and the seventh integer is 4. The average of those integers is (-2 + 4)/2 = 1.

Answer: D
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Re: The sum of seven consecutive integers is equal to 7. What is the avera   [#permalink] 12 Nov 2017, 08:49
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