A) 16
B) 4
C) 6
D) 1/3
Correct Answer: B
Solution :
(b): The sum of infinite number of terms in GP is given by \[{{S}_{\infty }}=\frac{a}{1-r}\] \[\Rightarrow \] \[6=\frac{a}{1-r}\] ... (1) Also the sum of square of the terms of the GP is given by \[{{S}_{\infty }}=\frac{{{a}^{2}}}{1-{{r}^{2}}}\] \[\Rightarrow \]\[18=\frac{{{a}^{2}}}{1-{{r}^{2}}}\] ? (2) Dividing (2) by square of (1) \[\Rightarrow \]\[\frac{1}{2}=\frac{1-r}{1+r}\] Applying component do dividend do, \[\frac{1+2}{1-2}=\frac{2}{-2r}\]\[\Rightarrow \]\[r=\frac{1}{3}\] \[\Rightarrow \]\[a=4\]You need to login to perform this action.
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