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(B) The given series is $5, 10, 20, 40, \ldots$This is a Geometric Progression $(G.P.)$ where the first term $a = 5$ and the common ratio $r = \frac{1

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$9^{th}$

Vedclass · Answer

(B) The given series is $5, 10, 20, 40, \ldots$This is a Geometric Progression $(G.P.)$ where the first term $a = 5$ and the common ratio $r = \frac{10}{5} = 2$.The $n^{th}$ term of a $G.P.$ is given by the formula $a_n = a \cdot r^{n-1}$.We need to find $n$ such that $a_n = 1280$.Substituting the values,we get $5 \cdot 2^{n-1} = 1280$.Dividing both sides by $5$,we get $2^{n-1} = \frac{1280}{5} = 256$.Since $256 = 2^8$,we have $2^{n-1} = 2^8$.Equating the exponents,$n - 1 = 8$,which gives $n = 9$.Therefore,$1280$ is the $9^{th}$ term of the series.

Fill in the blank space for the given series with the correct alternative.
Which term of the series $5, 10, 20, 40, \ldots$ is $1280$?

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Fill in the blank space for the given series with the correct alternative.Which term of the series $5, 10, 20, 40, \ldots$ is $1280$?