IIT-JEE 2007 | Sequences and Series Question 4 | Mathematics

1

IIT-JEE 2007

MCQ (Single Correct Answer)

+4

-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 ?

A

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

B

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

C

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

D

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

2

IIT-JEE 2007

MCQ (Single Correct Answer)

+4

-1

Let $$\,{V_r}$$ denote the sum of first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is (2r-1). Let $${T_r} = \,{V_{r + 1}} - \,{V_r} - 2\,\,\,and\,\,\,{Q_r} = \,{T_{r + 1}} - \,{T_r}\,for\,r = 1,2,...$$

$${T_r}$$ is always

A

an odd number

B

an even number

C

a prime number

D

a composite number

3

IIT-JEE 2007

MCQ (Single Correct Answer)

+4

-1

Let $$\,{V_r}$$ denote the sum of first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is (2r-1). Let $${T_r} = \,{V_{r + 1}} - \,{V_r} - 2\,\,\,and\,\,\,{Q_r} = \,{T_{r + 1}} - \,{T_r}\,for\,r = 1,2,...$$

The sum $${V_1}$$+$${V_2}$$ +...+$${V_n}$$ is

A

$${1 \over {12}}n(n + 1)\,(3{n^2} - n + 1)$$

B

$${1 \over {12}}n(n + 1)\,(3{n^2} + n + 2)$$

C

$${1 \over 2}n(2{n^2} - n + 1)$$

D

$${1 \over 3}(2{n^3} - 2n + 3)$$

4

JEE Advanced 2016 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-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

A

s > t and a₁₀₁ > b₁₀₁

B

s > t and a₁₀₁ < b₁₀₁

C

s < t and a₁₀₁ > b₁₀₁

D

s < t and a₁₀₁ < b₁₀₁

JEE Advanced Subjects