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

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

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

• A.M A
• Common ratio B
• Common difference C
• None of these D

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

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

The nth term of a G.P. is

• a₁rⁿ A
• a₁rⁿ⁺¹ B
• a₁r^n-1 C
• a₁r^-n D

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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 400 A
• 397 B
• 404 C
• 408 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

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

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

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

A sequence having no last term is called

• arithmetic sequence A
• Geometric sequence B
• Finite sequence C
• Infinite sequence D

• 
  A
• 
  B
• 
  C
• 
  D

If a, b, c are in A.P., then 3^a, 3^b, 3^care 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 common ration of a geometric sequence cannot be

• 0 A
• 1 B
• 2 C
• 3 D

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

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

An indicated sum of terms of a sequence is represented by

• Sn A
• an B
• S(n) C
• {Sn} D

If G is a G.M between a and b then a,G,b are in

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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

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

No term of a harmonic sequence can be

• 0 A
• 1 B
• 2 C
• 3 D

The general term of the A.P. is

• a₁+ (n - 1) d A
• n + (a₁- 1) d B
• d + (n - 1) a₁ C
• None of these D

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

• Finite terms A
• d<0 B
• Infinite terms C
• None of these D

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

• 136 A
• -136 B
• 148 C
• -148 D

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

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

An A.P. consists of n(odd terms) and its middle term is m. then the sum of the A.P. is

• 2 mn A
• 1/2 mn B
• mn C
• mn² 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

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

• 2 A
• 26 B
• 27 C
• 1 D

The third term of a G.P. is 4, The product of first five terms is

• 43 A
• 45 B
• 46 C
• None of these D