The sum of seven consecutive integers is equal to 7.

Question

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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fugaquasi · Answer

we can define the list of integers as {x, x+1 ...... x+6}

so the sum of this list would be: 7x+21

we are already given that the sum is equal to 7;

7x+21 = 7 => x+3=1 +> x=-2

Least integer: x=-2
Greatest Integer: x+6= -2+6 = 4

Average of least and greatest = (4-2)/2 = 2/2 = 1

imo (d)

BhavyaYadav · Answer

Let 7 consecutive terms be x,x+1, ..... x+6.
So sum = x+x+1+......+x+6 = 7
=> 7x+21 = 7
Also average = x+x+6/2 = 2x+6/2 = x+3 -(1)
=> 7(x+3) = 7
=> x+3 = 1
Thus average = 1 from (1).

arkadutt · Answer

it can be easily solved with a tad bit of guesswork.

we know, 1+2+3=6, and 3+4=7. since it's seven consecutive  integers

so, that leaves us with only this feasible option -- -2, -1, 0, 1, 2, 3, 4.

mean of smallest & largest numbers -> (-2+4)/2 = 1

Missinga · Answer

The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the sequence?

Let consecutive integers= a, a+1, a+2, a+3, a+4, a+5, a+6 
Sum of these integers= 7 
7a+21=7 
a=-2

Integers are -2,-1,0,1,2,3,4

Average of least and greatest= -2+4/2=2/2=1

D

Souradeep17 · Answer

7 consecutive integers: n ,n+1...n+6

Acc to ques.
7n+21=7
N=-2
Largest number -2+6=4
average=4+(-2)=2/2=1

Option D

GraemeGmatPanda · Answer

We call  a  be the first term, representing "seven consecutive integers" as  a,\ a+1,\ a+2,\ a+3,\ a+4,\ a+5,\ a+6 .
 a,\ a+1,\ a+2,\ a+3,\ a+4,\ a+5,\ a+6

We translate "The sum of seven consecutive integers is equal to 7" into  a + (a+1) + (a+2) + (a+3) + (a+4) + (a+5) + (a+6) = 7 .

This can be simplified to
 7a + 21 = 7

We solve the resulting linear equation for the unknown.
 7a = -14 
 a = -2

We identify the least and greatest terms by substituting  a  into the sequence.
 	ext{least term} = a = -2   	ext{greatest term} = a + 6 = 4

We use the average-of-first-and-last formula for evenly spaced integers to find the average of the least and greatest terms.
 \frac{-2 + 4}{2} = 1

Answer 1

Hope this helps! 
ʕ•ᴥ•ʔ

The sum of seven consecutive integers is equal to 7.

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The sum of seven consecutive integers is equal to 7.

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