ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 8 (Sequences and Series)

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

• 2⁹ A
• 2¹⁰ B
• 2¹¹ C
• 2⁸ D

If x,y are two positive distinct numbers then

• A>G>H A
• A<G<H B
• A=G=H C
• None of these D

The harmonic mean between a and b is

• 
  A
• 
  B
• 
  C
• 
  D

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

• A.P. A
• G.P. B
• H.P. C
• None of these D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 4 A
• 6 B
• 8 C
• 10 D

The difference of two consecutive terms of an A.P. is called ______

• General term A
• Common ratio B
• Common difference C
• None of these D

• 1/2 A
• 2 B
• 1/4 C
• 4 D

If x,y are two -ve distinct numbers then

• A>G>H A
• A<G<H B
• A=G=H C
• None of these D

The n numbers A₁,A₂,A₃,.....A_nare called an arithmetic means between a and b if a.A₁,A₂,A₃.....A_n, b is ______

• An arithmetic series A
• An arithmetic sequence B
• A geometric sequence C
• A harmonic sequence D

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

• 30 A
• 27 B
• 20 C
• 21 D

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

• Geometric sequence A
• Arithmetic series B
• Harmonic sequence C
• Harmonic series D

Geometric mean between a and b is

• 
  A
• 
  B
• 
  C
• 
  D

If a^x= b^y= c^zand a, b, c are in G.P. then x, y, z are in

• A.P. A
• G.P. B
• H.P. C
• None of these D

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

• 8 A
• 4 B
• -4 C
• 8 D

If a, b, c are in AP., a, b, c are in G.P. then A, m²b, c are in

• A.P. A
• G.P. B
• H.P. C
• None of these D

The formula an = arn-1represents

• nth term of G.P A
• Sum of the first n terms B
• G.M between a and b C
• None of these D

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

• nth term of an A.P A
• Sum of first n terms B
• A,M between a and b C
• None of the above D

The difference of two consecutive terms of an A.P is called the

• Common difference A
• Common ratio B
• Geometric series C
• Geometric mean D

A number A is called the arithmetic mean between a and b if a, A, b is ______

• Arithmetic sequence A
• Geometric sequence B
• Harmonic sequence C
• Arithmetic sequence D

An infinite sequence has no

• nth term A
• Last term B
• Sum C
• None of these D

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

• A. P. A
• G. P. B
• H. P. C
• None of these D

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

• n = 1∀n∈ N A
• n>1∧n∈N B
• n∈Z C
• None of the above D

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

• 2 and 12 A
• 1 and 10 B
• 3 and 11 C
• -7 and 2 D

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

• Series A
• Function B
• Real sequence C
• Range D

an -an-1,∀n∈N∧n>1 in an A.P is called

• Common difference A
• nth term B
• Common ratio C
• None of these D

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

• Harmonic Series A
• Oscillatroy Series B
• Arithmetic Series C
• None of these D

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

• 125 A
• 107 B
• 108 C
• 113 D

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

• n, a, b A
• n, a B
• n, b C
• n D

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

• Infinite series A
• Arithmetic series B
• Geometric series C
• Harmonic series D