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

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

Find the next two terms of 7, 9, 12, 16,...

• 18, 20 A
• 19, 22 B
• 20, 25 C
• 21, 27 D

Geometric mean between a and b is

• 
  A
• 
  B
• 
  C
• 
  D

The A.M. of two numbers is 34 and G.M. is 16, the numbers are

• 2 and 64 A
• 64 and 3 B
• 64 and 4 C
• None of these D

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

• 26 A
• 7 B
• 21 C
• Cannot be determined D

A function whose domain is a subset of natural numbers is called ______

• Identity function A
• Sequence B
• Onto function C
• Series 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

• 2²- n - 1 A
• 1 - 2^-n B
• n + 2^-n-1 C
• 2ⁿ- 1 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

If #n = (n-5)2 + 5, then find #3 x #4.

• 54 A
• 12 B
• 4 C
• 9 D

The 6th term of an arithmetic sequence whose first term is 3 and common difference in zero is

• 18 A
• 6 B
• 3 C
• 0 D

H.M. between 3 and 7 is

• 
  A
• 
  B
• 
  C
• 
  D

5th term of a G.P. is 2, then the product of first 9 terms is

• 256 A
• 128 B
• 512 C
• None of these D

Write the first four terms of the arithmetic sequence 5, 2, -1, ... is

• 3 A
• -4 B
• 7 C
• 1 D

An infinite arithmetic series is always

• Convergent A
• Oscillatory B
• Divergent C
• None of these D

If a,b,c are in arithmetic progression, then 1/a,1/b.1/c are in

• A.M A
• G.M B
• H.M C
• G.P D

If b₁, b₂, b₃, ... are in G.P. with first term unity and common ratio r, then the minimum value of b₁- b₃+ b₅is equal to

• 3/4 A
• 1/4 B
• 1 C
• None of these D

Sum of first n terms of an arithmetic series is

• 
  A
• 
  B
• 
  C
• 
  D

The general term of a sequence is denoted by

• a₁ A
• a_n B
• n C
• s_n D

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

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  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

The number of divisors of 1029, 1547 and 122 are in

• A.P. A
• G.P. B
• H.P. 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

A sequence whose reciprocal is an A.P is called

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

The5thand 13th terms of an A.P are 5 and-3 respectively The first term of the A.P is

• 1 A
• -15 B
• 9 C
• 2 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

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

If 6th term of a series in A.P, is -2 and 8th term is -8, the first term of the serie is

• 13 A
• -13 B
• 18 C
• -10 D