IIT-JEE 2007 | Sequences and Series Question 6 | Mathematics

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IIT-JEE 2007

MCQ (Single Correct Answer)

-1

Let $${A_1}$$, $${G_1}$$, $${H_1}$$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $$n \ge 2,\,Let\,{A_{n - 1}}\,\,and\,\,{H_{n - 1}}$$ have arithmetic, geometric and harminic means as $${A_n},{G_n}\,,{H_n}$$ repectively.

Which one of the following statements is correct ?

$${G_1} > {G_2}\, > {G_3} > ...$$

$${G_1} < {G_2}\, < {G_3} < ...$$

$${G_1} = {G_2}\, = {G_3} = ...$$

$${G_1} < {G_2}\, < {G_3} < ...$$ and $${G_1} > {G_2}\, > {G_3} > ...$$

JEE Advanced 2016 Paper 2 Offline

MCQ (Single Correct Answer)

-1

Let b_i > 1 for I = 1, 2, ......, 101. Suppose log_eb₁, log_eb₂, ......., log_eb₁₀₁ are in Arithmetic Progression (A.P.) with the common difference log_e2. Suppose a₁, a₂, ......, a₁₀₁ are in A.P. such that a₁ = b₁ and a₅₁ = b₅₁. If t = b₁ + b₂ + .... + b₅₁ and s = a₁ + a₂ + ..... + a₅₁, then

s > t and a₁₀₁ > b₁₀₁

s > t and a₁₀₁ < b₁₀₁

s < t and a₁₀₁ > b₁₀₁

s < t and a₁₀₁ < b₁₀₁

IIT-JEE 2012 Paper 2 Offline

MCQ (Single Correct Answer)

-1

Let $${a_1},{a_2},{a_3},.....$$ be in harmonic progression with $${a_1} = 5$$ and $${a_{20}} = 25.$$ The least positive integer $$n$$ for which $${a_n} < 0$$ is

IIT-JEE 2009 Paper 2 Offline

MCQ (Single Correct Answer)

-1

If the sum of first $$n$$ terms of an A.P. is $$c{n^2}$$, then the sum of squares of these $$n$$ terms is

$${{n\left( {4{n^2} - 1} \right){c^2}} \over 6}$$

$${{n\left( {4{n^2} + 1} \right){c^2}} \over 3}$$

$${{n\left( {4{n^2} - 1} \right){c^2}} \over 3}$$

$${{n\left( {4{n^2} + 1} \right){c^2}} \over 6}$$

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