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There are n A.M.'s between 7 and 85 such that (n-3)th mean :nth mean is as 11:24; find n

There are n A.M.'s between 7 and 85 such that (n-3)th mean :nth mean is as 11:24; find n 
 

Grade:11

1 Answers

Aditya Gupta
2081 Points
5 years ago
7, a2, a3, a4, …., an+1, 85 are in AP
 (n-3)th mean is an-2
nth mean is an+1.
ar= 7+(r-1)d
an+2=85= 7+(n+1)d
so 78=(n+1)d
or d=78/(n+1)
(n-3)th mean :nth mean= (7+(n-3)d)/(7+nd)=11/24
now simply replace d in terms of n and solve for n to obtain n=5

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