Question
Fri November 11, 2011 By:

If 1 by x+2, 1 by x+3 and 1 by x+5 are in AP. Find the value of x.

Expert Reply
Fri November 11, 2011
1/(x+2) , 1/(x+3) and 1/(x+5) are in AP.
 
Therefore
 
First term = 1/(x+2)
 
Second Term = 1/(x+3)
 
Third term = 1/(x+5)
 
Common Difference , d = T3 - T2  = T2  - T1
 
This means
 
d= 1/(x+5) - 1/(x+3) = 1/(x+3) - 1/(x+2)
 
Hence, take LCM on both sides we get
 
x+3-x-5/(x+5)(x+3) = x+2-x-3/(x+3)(x+2)
 
-2/(x+5) = -1/(x+2)
 
Cross multiply and we get
 
2(x+2) = x+5
 
2x + 4 = x + 5
 
x = 1
 
This is the answer
 
Thank you
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