Question # 1

Given two numbers a and b. Let A denote the single A.M. between these and S denote the sum of n A.M.'s between them. Then S/A depends upon

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n, a, b

n, a

n, b

n

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The numbers of G₁, G₂, G₃...... G_nare called n geometric means between a and b is a, G₁, G_2,G₃, ... G_n, b are in

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H.P.

A.P.

G.P.

None of these

If all members of a sequence are real numbers then it is called a

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Series

Function

Real sequence

Range

The sum of an indicated number of terms in a sequence is called

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sequence

progression

Series

Mean

Find the sum of the infinite geometric series 2 + 1 + 0.5 + ....

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3.5

3

4

None of these

No term of a geometric sequence can be

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0

1

2

3

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2

-3/2

1

0

The formula an = a +(n-1)d for an A.P is called

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nth term of an A.P

Sum of first n terms

A,M between a and b

None of the above

If all members of a sequence are real numbers then it is called

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A.P

Real Sequence

G.P

None of these

The third term of the sequence a_n= (-1)^n-1(n-7) is ______

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8

4

-4

8

The series obtained by adding the terms of an arithmetic sequence is called the

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Infinite series

Harmonic series

Geometric series

Arithmetic series

A series consisting of an unlimited number of terms is termed as an

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Finite sequence

Infinite sequence

^{Infinite series}

geometric sequence

If a₁= 3, r = 2, then the nth term of the G.P. is

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2.3^n-1

3.2ⁿ

3.2ⁿ⁺¹

3.2^n-1

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1

2

3/2

5/2

Let the sequence 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, ..... where n consecutive terms have the value n, then 1025th term is

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2⁹

2¹⁰

2¹¹

2⁸

If a₁, r are first term and the common ratio respectively then the sum of an infinite geometric series is

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The 26th term of the A.P -2,-4,10,.............is

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136

-136

148

-148

The sum of all 2 digit number is

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4750

3776

4895

4905

The formula an = arn-1represents

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nth term of G.P

Sum of the first n terms

G.M between a and b

None of these

How many numbers are there between 103 and 750 which are divisible by 6

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125

107

108

113

In an A.P,a +(n-a)d is

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1st term

General term

Last term

None of these

The series obtained by adding the terms of a geometric sequence is called

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Infinite series

Arithmetic series

Geometric series

Harmonic series

If 5,7 and 9 are A.Ms between a and b, then a and b is equal to

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2 and 12

1 and 10

3 and 11

-7 and 2

A sequence is a functions whose domain is a subset of the set of

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Natural numbers

Real numbers

Whole numbers

Rational numbers

The general term of the A.P. is

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a₁+ (n - 1) d

n + (a₁- 1) d

d + (n - 1) a₁

None of these

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The nth term of a G.P. is

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a₁rⁿ

a₁rⁿ⁺¹

a₁r^n-1

a₁r^-n

A Geometric Series is divergent only if

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|r|>1

|r|≥1

|r|=1

None of these

An infinite arithmetic series is always

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Convergent

Oscillatory

Divergent

None of these

No term of a harmonic sequence can be

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0

1

2

3

A sequence of number whose reciprocals form an arithmetic sequence is called

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Geometric sequence

Arithmetic series

Harmonic sequence

Harmonic series

Let S_ndenote the sum of the first n terms of an A.P. If S_2n= 3 S_n: S_nis equal to

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4

6

8

10

Let a₁, a₂, a₃, a₄and a₅be such that a₁, a₂, and a₃are in A.P., a₂, a₃and a₄are in G.P and a₃, a₄and a₅are in H.P. Then, a₁, a₃and a₅are in

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G.P.

A.P.

H.P.

None of these

The consecutive terms of a progressions are 30, 24, 20. The next term of the progression is

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The next term of the sequence 1, 2, 4, 7, 11, ..... is.

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15

16

17

18

Find the geometric mean between 4 and 16

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If a, b, c are in A.P., then 3^a, 3^b, 3^care in

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A.P.

G.P.

H.P.

None of these