Consider a sequence of seven consecutive integers

Question

Consider a sequence of seven consecutive integers. The average of the first five integers is  n . The average of all the seven integers is:

A.  n 
B.  n+1 
C.  k*n , where  k  is a function of  n 
D.  n+\frac{2}{7} 
E.  n+2

HKD1710 · Answer

In case of a set of consecutive numbers, Middle number = Average of set

Set of 5 numbers - a, a+1,  a+2 , a+3, a+4
Middle number = Average = a+2

but we are given that average for first 5 numbers is = n

hence a+2 = n

Set of 7 numbers - a, a+1, a+2,  a+3 , a+4, a+5, a+6
Middle number = Average = a+3 = (a+2) + 1 =  n+1

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Consecutive numbers are in A.P. and sum for such a set = number of terms * (first term + last term) / 2

If we divide the sum by number of terms then we get average. hence average = (first term + last term) / 2

Set of 5 numbers - a, a+1,  a+2 , a+3, a+4
Average = (first term + last term) / 2 = (a + a+4) / 2 = a+2
Average = a+2 = n

Set of 7 numbers - a, a+1, a+2,  a+3 , a+4, a+5, a+6
Average = (first term + last term) / 2 = (a + a+6) / 2 = a+3 = (a+2)+1
Average =  n + 1

niks18 · Answer

OE

Average of consecutive numbers in an ODD sequence = Middle number of the sequence 
Let the seven consecutive integers be  1,2,3,4,5,6,7 . Hence average of this sequence  = 4 
First five integers of the above sequence are  1,2,3,4,5 . Average of this sequence  = 3 = n 
Clearly,  4 = 3 +1 = n+1

Hence Option  B

gracie · Answer

average of first five integers=middle (third) term=n
average of seven integers=middle (fourth) term=n+1
B

gblessing · Answer

This is perhaps another interpretation that I thought I would suggest:

Consider a sequence of seven consecutive integers. The average of the first five integers is n.

The above can be restated as the first five integers are n-2, n-1, n, n+1, n+2. Knowing the final two numbers in the sequence are n+3 and n+4, eliminate option A.

Substitution to find the correct answer out of B to E
5 (n-2) + 6 (n-1) + 7 (n) + 8 (n+1) + 9 (n+2) + 10 (n+3) + 11 (n+4) = 56. 56/7 (total number of terms in sequence)=8. 8 is n+1, so option B

Consider a sequence of seven consecutive integers

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