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The sum of the intercepts cut off by the axes on the lines $x + y = a, x + y = a r, x + y = a r^{2}, \dots$ where $a \neq 0$ and $r = 1 / 2$ is

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22a

a/2

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detailed solution

Correct option is C

The intercepts between the axes made by the given lines are a2,ar2,ar22,…So the required sum =2a+ar+ar2+…=2a1−r=2a1−(1/2)=22a

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The sum of the intercepts cut off by the axes on the lines x+y=a,x+y=ar,x+y=ar2,… where a≠0 and r=1/2 is

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The sum of the intercepts cut off by the axes on the lines $x + y = a, x + y = a r, x + y = a r^{2}, \dots$ where $a \neq 0$ and $r = 1 / 2$ is