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Question

If r>1 and
x=a+ar+ar2
y=b+br+br2
z=c+cr+cr2,

then the value of xyz2 is ___.


A

abc2

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B

abrc

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C

abc2r

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D

abc

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Solution

The correct option is A

abc2


Here, we will calculate the value of x,y and z in terms of a,b,c and r.
The sum of a GP with first term a and common ratio r is given by
S=a1r.

x=a1r

y=b1r

z=c1r

xyz2=a(1r)×b(1r)c2(1r)2

=abc2


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