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Question

Let xn,yn,zn,wn denote nth terms of four different arithmetic progressions with positive terms. If x4+y4+z4+w4=8 and x10+y10+z10+w10=20 then the maximum value of x20y20z20w20 is

A
104
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B
106
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C
108
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D
1010
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Solution

The correct option is A 104
We know that sum of two A.P's will also be an A.P, so
x4+y4+z4+w4=A+3D=8......(i)
x10+y10+z10+w10=A+9D=20.....(ii)
Using equation (i) and (ii),
A=2,D=2
Now,
x20+y20+z20+w20=A+19D=40
We know that A.MG.M
x20+y20+z20+w204(x20y20z20w20)14
Hence x20y20z20w20104

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