A bag has written a sequence of consecutive natural numbers. The numbers of the elements in the sequence is equal to the smallest element among them doubled and subtracted by 2. The arithmetic mean of the sequence is 12.5. What is the greatest written number?
Answers
Given : A bag has written a sequence of consecutive natural numbers. The number of elements in the sequence is equal to the smallest element among them doubled and subtracted by 2.
The arithmetic mean of the sequence is 12.5.
To Find : the greatest written number
Solution:
Let say numbers are a , a + 1 , a + 2 and so on till a + n - 1
n = number of elements
n = 2 (a) - 2
n = 2a - 2
a + n - 1 = a + (2a - 2) - 1 = 3a - 3
First term = a
Last term = 3a - 3
number of term = n
Sum = (n/2) (a + 3a - 3) = (n/2)( 4a - 3)
Mean = (n/2)( 4a - 3) /n
= ( 4a - 3) /2
( 4a - 3) /2 = 12.5
=> 4a - 3 = 25
=> 4a = 28
=> a = 7
Last term = 3a - 3 = 3(7) - 3 = 18
the greatest written number is 18
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