The value of x+y+z is 15 if a,x,y,z,b are in A.P. while the value of 1x+1y+1z is 53 if a,x,y,z,b are in H. P. Then the value of and b are
1 and 9
As x,y,z, are A.M. of a and b
∴x+y+z=3(a+b2)∴15=32(a+b)⇒a+b=10 ...(i)Again 1x,1y,1z are A.M.of 1a and 1b∴1x+1y+1z=32(1a+1b)∴53=32.a+bab⇒109=10ab⇒ab=9 ...(ii)
Solving (i) and (ii), we get
a = 9, 1, b = 1, 9