If b is the first term of an infinite G.P. wh | vedclass

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(C) Let the first term be $b$ and the common ratio be $r$.For an infinite geometric progression $(G.P.)$ to have a finite sum,the condition $|r| < 1$

Vedclass · Accepted Answer

$( 0, 10 )$

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(C) Let the first term be $b$ and the common ratio be $r$.For an infinite geometric progression $(G.P.)$ to have a finite sum,the condition $|r| The sum of an infinite $G.P.$ is given by the formula $S = \frac{b}{1 - r}$.Given $S = 5$,we have $\frac{b}{1 - r} = 5$.Rearranging for $r$,we get $1 - r = \frac{b}{5}$,which implies $r = 1 - \frac{b}{5}$.Substituting the condition $-1 $-1 Subtracting $1$ from all parts: $-2 Multiplying by $-5$ (and reversing the inequality signs): $0 Thus,$b$ lies in the interval $(0, 10)$.

If $b$ is the first term of an infinite $G.P.$ whose sum is $5$,then $b$ lies in the interval

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