(C) The given sequence is a Geometric Progression $(GP)$ where the first term $a = 6$.The common ratio $r$ is calculated as $r = \frac{12}{6} = 2$.The

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(C) The given sequence is a Geometric Progression $(GP)$ where the first term $a = 6$.The common ratio $r$ is calculated as $r = \frac{12}{6} = 2$.The formula for the $n^{th}$ term of a $GP$ is $T_n = a \times r^{n-1}$.To find the $7^{th}$ term $(n = 7)$:$T_7 = 6 \times 2^{7-1} = 6 \times 2^6$.Since $2^6 = 64$,we have:$T_7 = 6 \times 64 = 384$.

Competitive Quantitative Aptitude Progression and Sequence Progression and Sequence

Medium

Write the seventh term of the following $GP$: $6, 12, 24, 48, \ldots$

A
$192$
B
$96$
C
$384$
D
$48$

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Progression and Sequence

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Progression and Sequence

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Write the seventh term of the following $GP$: $6, 12, 24, 48, \ldots$

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The sum of the series $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \dots$ up to $15$ terms is

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