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If the sum of an infinite decreasing G.P. is 3 and sum of the cubes of its terms is 108/13, then common ratio is given by
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a
15
b
14
c
13
d
12
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Correct option is C
a1−r=3,a31−r3=10813 where |r|<1∴27(1−r)31−r3=10813⇒1−2r+r21+r+r2=413⇒13−26r+13r2=4+4r+4r2⇒9r2−30r+9=0⇒3r2−10r+3=0.⇒(3r−1)(r−3)=0⇒r=1/3 [∵|r|<1]Similar Questions
If the roots of the equation,
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