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

• 1/2 A
• 2 B
• 1/4 C
• 4 D

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

• 8 A
• 4 B
• 4 C
• 16 D

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

• 1st term A
• General term B
• Last term C
• None of these D

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

• 
  A
• 
  B
• 
  C
• 
  D

Write the first four terms of the sequence if a_n= (-1)ⁿn²

• -1, 4, -9, 16 A
• 1, -4, 9, 16 B
• 1, 4, 9, 16 C
• None of these D

Sum of first n terms of an arithmetic series is

• 
  A
• 
  B
• 
  C
• 
  D

• 1 A
• 2 B
• 3/2 C
• 5/2 D

Geometric mean between a and b is

• 
  A
• 
  B
• 
  C
• 
  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

The 31 term of the A.P 5,2,-1.....is

• -82 A
• 82 B
• 85 C
• -85 D

If p, q, r and in A.P., a is G.M. between p and q and b is G.M. between q and r, then a², q², b²are in

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

The sum of n terms of a series is denoted by

• d A
• n B
• S_n C
• a_n D

If a_n= 2n -3, write the first four terms

• -3, -1, 1, 3 A
• 1, 3, 5, 7 B
• -1, 1, 3, 5 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

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

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

p, q, r and s are integers. If the A.M. of the roots of x2- px + q2= 0 and G.M. of the roots of x2- rx + s2= 0 are equal, then

• q is an odd integer A
• r is an even integer B
• p is an even integer C
• s is an odd integer D

The 10th common term between the series 3+7+11+....... and 1 + 6 +11 + ....... is

• 191 A
• 193 B
• 211 C
• None of these D

No term of a harmonic sequence can be

• 0 A
• 1 B
• 2 C
• 3 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

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 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

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

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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• xyz A
• 0 B
• 1 C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

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 a₁, r and a_nare the first term, common ratio and the nth term respectively of a G. P. then a_n=

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