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

(1)n (2) n+1
(3) K*n, where K is a function
of n (4) n+(2/7)

Solution follows here:
Solution:

Given that it is a sequence of 7
consecutive integers. As the average of first five integers is n, sum of first
five integers is 5n.

=> t

_{1}+t_{2}+t_{3}+t_{4}+t_{5}= 5n ------(1)
As they are consecutive integers, the
middle number of the first five numbers is nothing but average of the five
numbers ie., ‘n’.

=> t

_{3}= n => t_{4}= n+1 => t_{5}= n+2 => t_{6}= n+3 => t_{7}= n+4
=> t

_{6}+t_{7}= n+3+n+4 = 2n+7 ------(2)
Adding (1) and (2),

t

_{1}+t_{2}+t_{3}+t_{4}+t_{5}+t_{6}+t_{7}= 5n+2n+7 = 7n+7
=> Average of all 7 numbers = (t

_{1}+t_{2}+t_{3}+t_{4}+t_{5}+t_{6}+t_{7})/7 = n+1**Answer (2)**
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