COMEDK 2025 Evening Shift | Sequences and Series Question 1 | Mathematics

A geometric progression consists of an even number of terms. If the sum of all the terms is five times the sum of the terms occupying the odd places, then the common ratio of the geometric progression is

$r=4$

$r=3$

$r=6$

$r=2$

COMEDK 2025 Evening Shift

MCQ (Single Correct Answer)

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Given that n number of arithmetic means are inserted between two pairs of numbers $a, 2 b$ and $2 a, b$; where $a, b \in R$. If the $m^{\text {th }}$ means in the two cases are the same, then the ratio $a: b$ is equal to

$m:(n-m+1)$

$n:(n-m+1)$

$(n-m+1): m$

$(n-m+1): n$

COMEDK 2025 Afternoon Shift

MCQ (Single Correct Answer)

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The terms of an infinitely decreasing geometric progression in which all the terms are positive, the first term is $\mathbf{4}$, and the difference between third and fifth term is $\frac{32}{81}$, then which of the following is not true

$S_{\infty}=3+2 \sqrt{2}$

$r=\frac{1}{3}$

$S_{\infty}=6$

$r=\frac{2 \sqrt{2}}{3}$

COMEDK 2025 Morning Shift

MCQ (Single Correct Answer)

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$0.2+0.22+0.022+\ldots \ldots \ldots$. up to $n$ terms is equal to

$\frac{2}{9}-\frac{2}{81}\left(1-10^{-n}\right)$

$\frac{2}{9}\left[n-\frac{1}{9}\left(1-10^{-n}\right)\right]$

$\frac{2}{9}\left(1-10^{-n}\right)$

$\frac{n}{9}\left(1-10^{-n}\right)$

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