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

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Bunuel
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The sum of seven consecutive integers is equal to 7. What is the avera [#permalink] The sum of seven consecutive integers is equal to 7. What is the avera   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
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D
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Re: The sum of seven consecutive integers is equal to 7. What is the avera [#permalink] The sum of seven consecutive integers is equal to 7. What is the avera   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] The sum of seven consecutive integers is equal to 7. What is the avera   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] The sum of seven consecutive integers is equal to 7. What is the avera   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] The sum of seven consecutive integers is equal to 7. What is the avera   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] The sum of seven consecutive integers is equal to 7. What is the avera   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] The sum of seven consecutive integers is equal to 7. What is the avera   12 Nov 2017, 08:49
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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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The sum of seven consecutive integers is equal to 7. What is the avera [#permalink] The sum of seven consecutive integers is equal to 7. What is the avera   22 Nov 2017, 22:56
let the lowest no be x
since the set contains subsequent integers we have
x, x+1, x+2,x+3,x+4,x+5,x+6=7(sum of consequtive integers)
7x+21=7
7x=7-21=-14
x=-14/7=-2
lowest number is -2 other numbers are -1,0,1,2,3,4
lowest+highest/2=-2+4/2=1=average.
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The sum of seven consecutive integers is equal to 7. What is the avera [#permalink] The sum of seven consecutive integers is equal to 7. What is the avera   23 Nov 2017, 04:51
Sum of consecutive values= n*Average of the first and the last term
7= 7(First+last)/2
1=(First+Last)/2

D
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Re: The sum of seven consecutive integers is equal to 7. What is the avera [#permalink] The sum of seven consecutive integers is equal to 7. What is the avera   23 Nov 2017, 06:06
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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


Sum of 7 consecutive integers is 7. But if you try to add numbers such as 1, 2, 3,... the sum will be much higher. Hence, there must be some negative integers to cancel off some positive integers and get a sum as low as 7.

A little bit of thought will show that the integers must be -2, -1, 0, 1, 2, 3, 4
So sum = 3+4 = 7

Average of least and greatest numbers = (-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] The sum of seven consecutive integers is equal to 7. What is the avera   23 Nov 2017, 07:16
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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



Hi..

since the terms are CONSECUTIVE, the average of all 7 is EQUAL to average of the largest and smallest integer..
average of all 7 \(= \frac{7}{7} =1 =\) average of the largest and smallest integer..
ans 1...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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