The average of 'n' consecutive natual numbers starting from 1, changed from 6 to 6.5, after the next number is added. What is this new number?
Answers
Answer:
calculating the average of 1 , 2 , 3 , 4 ,5 ,…………… , N.
Sum of these numbers = N.(N+1)/2
Let she added a number x (belongs to N) twice by mistake and obtained a
wrong average 31/5. Thus ,the sum of the numbers= (31/5).N , acordingly:-
(31/5).N- N.(N+1)/2 = x. , dividing both sides by N.
or. 31/5 = x/N + (N+1)/2………………..(1)
In eqn. (1) there is 31/5 in left side in which Dr is 5, and there is N and 2 are in
right sides Dr. So that (to calculate N and. x ) value of N will be a multiple of
5 (as. 5 , 10 , 15 ,……) .
Putting N=5 in eqn. (1)
31/5=x/5+(5+1)/2
or. 31/5–3=x/5. => x=16 (16 belongs to N ,but not possible as numbers are 1 to 5
only).
Now putting N=10 in eqn. (1)
31/5. = x/10+ (10+1)/2
or. 31/5 -11/2=x/10
or (62–55)/10= x/10 => x = 7 (7 belongs to N , also possible as numbers are 1 to 10)
Thus , the number she added twice was = 7.
Explanation:
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Answer:
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