Question # 1

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

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

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15

16

17

18

if a₁ =3, d=7 and a_n =59 , then the number of terms in A.P is

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7

9

11

13

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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2²- n - 1

1 - 2^-n

n + 2^-n-1

2ⁿ- 1

If S_rdenotes the sum of the first r terms of a G.P., then S_n, S_2n- S_n, S_3n- S_2nare in

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A.P.

G.P.

H.P.

None of these

If A is such that a,A,B are in A.P then A is called

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A.M

Common ratio

Common difference

None of these

an - an-1 will be common difference in an A.P if

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n = 1∀n∈ N

n>1∧n∈N

n∈Z

None of the above

The common ration of a geometric sequence cannot be

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0

1

2

3

If x, y, z are the pth, qth, rth terms of an A.P. and also of G.P., then x^y-z. y^z-x. z^x-yeqals

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xyz

0

1

None of these

The fifth term of the sequence a_n= 2n + 3 is ______

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13

-13

8

3

If x,y are two -ve distinct numbers then

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A>G>H

A<G<H

A=G=H

None of these

G is geometric mean between a and b if a, G, b is

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A.P.

G.P.

H.P.

None of these

The nth term of an A.P., is 12-4n. Its common difference is

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8

4

16

What is the 26th term of the sequence, if its general term is a_{n = (-1)}ⁿ⁺¹

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2

26

27

1

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0

1

2

3

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

Which term of the A.P 5,8,11,24.............is 320

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104th

106th

105th

64th

A Series which does not coverage to a Unique sum is called

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Harmonic Series

Oscillatroy Series

Arithmetic Series

None of these

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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

Sum of n terms of a geometric series if | r | < 1 is

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The sixth term of the sequence 1,3,12,60....is

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1500

72

2160

2520

If x,y are two positive distinct numbers then

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A>G>H

A<G<H

A=G=H

None of these

The sum of the squares of three distinct real numbers, which are in G.P., is S². if their sum isαS then

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If A, G, H are the arithmetic, geometric and harmonic means between a and b respectively then A, G, H are in

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A. P.

G. P.

H. P.

None of these

How many term are there in the A.P, in which a₁ = 11 , a_n =68, d=3

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30

27

20

21

H₁, H₂, H₃, .... H_nare called n harmonic means between a and b if a, H₁, H₂, H₃, ... H_nb are in

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H.P.

G.P.

A.P.

None of these

If P, Q, R be the A.M., G.M., H.M. respectively between any two rational numbers a and b, then P - Q is

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If a₁and r are the first term and the common ratio respectively then (n + 1)th term of the G.P. is

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0

a₁r^n-1

a₁rⁿ⁺¹

a₁rⁿ

3, 6, 12,.... is

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A.P

G.P.

H.P.

None of these

The nth term of an A.P is (3n+5) Its 75th term is

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26

7

21

Cannot be determined

For an arithmetic series to be convergent it is necessary that the series has

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Finite terms

d<0

Infinite terms

None of these

The fifth term of an A.P. Whose first term is 5 and common difference is 3,is

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20

17

25

30

The sum of first twenty odd integers in A.P is

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400

397

404

408

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The three consecutive numbers a,√ab,b are in

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G.P

H.P

G.M

None of these