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

If a₁= 3, r = 2, then the nth term of the G.P. is

• 2.3^n-1 A
• 3.2ⁿ B
• 3.2ⁿ⁺¹ C
• 3.2^n-1 D

In following question, a number series is given with one term missing. choose the correct alternative that will same pattern and fill in the blank spaces.1 , 4, 9, 16, 25, x

• 35 A
• 36 B
• 48 C
• 49 D

• 12 A
• 13 B
• 14 C
• 15 D

The harmonic mean between a and b is

• 
  A
• 
  B
• 
  C
• 
  D

Geometric mean between a and b is

• 
  A
• 
  B
• 
  C
• 
  D

Which one represents a sequence

• an A
• Sn B
• a(n) C
• {an} D

Every term of a G.P. is positive and also every term is the sum of two preceding terms. Then the common ratio of the G.P. is

• 
  A
• 
  B
• 
  C
• 
  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

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

• A.P A
• Real Sequence B
• G.P 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

An infinite arithmetic series is always

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

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

Find the sum of the infinite geometric series 2 + 1 + 0.5 + ....

• 3.5 A
• 3 B
• 4 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 sum of first 60 natural numbers is

• 1830 A
• 3660 B
• 1640 C
• 1770 D

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

• 8 A
• 4 B
• 4 C
• 16 D

• 2 A
• -3/2 B
• 1 C
• 0 D

• 
  A
• 
  B
• 
  C
• 
  D

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

• 13 A
• -13 B
• 8 C
• 3 D

If a₁= a₂= 2, a_n= a_n-1- 1 (n > 2), then a₅is

• 1 A
• 0 B
• -1 C
• -2 D

For an A.P common difference d

• Can be zero A
• May or may not zero B
• Cannot be zero C
• None of these D

The sides of a right angled triangle are in A.P The ratio of sides is

• 1:2:3 A
• 3:4:5 B
• 2:3:4 C
• 5:8:3 D

H.M. between 3 and 7 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 7th term of the A.P 7,11,15,is

• 24 A
• 31 B
• 26 C
• 23 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

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

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

• 
  A
• 
  B
• 
  C
• 
  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