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

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 common ration of a geometric sequence cannot be

• 0 A
• 1 B
• 2 C
• 3 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 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

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

An infinite arithmetic series is always

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

1,1/3,1/5,1/7,1/9..... is a

• geometric sequence A
• finite sequence B
• infinite sequence C
• arithmetic series D

The harmonic mean between a and b is

• 
  A
• 
  B
• 
  C
• 
  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

if a₁ =3, d=7 and a_n =59 , then the number of terms in A.P is

• 7 A
• 9 B
• 11 C
• 13 D

Sum of first n terms of an arithmetic series is

• 
  A
• 
  B
• 
  C
• 
  D

The sum of indicated terms of a sequence is called

• Arithmetic series A
• Series B
• Harmonic series 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

• 15/23 A
• 7/15 B
• 7/8 C
• 15/7 D

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

• 1 A
• 0 B
• -1 C
• -2 D

The sum of infinite numbers of terms of an arithmetic series is

• Finite A
• Infinite B
• May or may not finite C
• None of these D

If three unequal numbers p, q, r are in H.P. and their squares are in A.P., then the ration p : q : r is

• 
  A
• 
  B
• 
  C
• 
  D

• 12 A
• 13 B
• 14 C
• 15 D

The element range of sequence are called

• Series A
• progression B
• Members C
• Terms 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

Which term of the A.P 5,8,11,24.............is 320

• 104th A
• 106th B
• 105th C
• 64th 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

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

The sum of all 2 digit number is

• 4750 A
• 3776 B
• 4895 C
• 4905 D

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

• 
  A
• 
  B
• 
  C
• 
  D

If a₁and r are the first term and the common ratio respectively then (n + 1)th term of the G.P. is

• 0 A
• a₁r^n-1 B
• a₁rⁿ⁺¹ C
• a₁rⁿ 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

If Sn is a definite number as n → ∞,then the geometric series is

• Convergent A
• Divergent B
• Oscillatroy 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

The fifth term of an A.P. Whose first term is 5 and common difference is 3,is

• 20 A
• 17 B
• 25 C
• 30 D