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Question

If numbers n-2 , 4n-1 and 5n+2 are in AP. Find the value of n and its next two terms.


Solution

Since (n-2), ( 4n-1) and (5n+2) in A.P.

So, 4n-1 - (n- 2) = 5n+2 -(4n-1)

= 4n-1-n+2 = 5n+2-4n+1

= 4n -n -5n + 4n = 2+1-2+1

= 2n = 2

n=1

1st term = n-2= 1-2 =-1
2nd term =4n-1=4-1=3
3rd term =5n+2=5+2=7
so d=3-(-1)=4 

4th term = a+3d = -1+(3×4)= 11
5th term = a+4d =-1+(4×4) =15


 

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