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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesG.P.Medium2 minQB

MathematicsMediumsingle choice

The first term of an infinite G.P. is 1 and every term is equal to the sum of the successive terms. Then its fourth term will be

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Solution:

G.P.: $1, r, r^{2}, r^{3}, \dots$ Each term equals the sum of all terms after it, so $1 = r + r^{2} + r^{3} + \dots = \frac{r}{1 - r}$ . $1 - r = r \Rightarrow r = \frac{1}{2}$ , so $T_{4} = r^{3} = \frac{1}{8}$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:G.P.

⏱ 2mℹ️ Source: QB

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