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

If S_rdenotes the sum of the first r terms of a G.P., then S_n, S_2n- S_n, S_3n- S_2nare in

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

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

Geometric mean between a and b is

• 
  A
• 
  B
• 
  C
• 
  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

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

• 
  A
• 
  B
• 
  C
• 
  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 sum of n terms of a series is denoted by

• d A
• n B
• S_n C
• a_n D

• 
  A
• 
  B
• 
  C
• 
  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

For three consecutive terms in A.P middle term is called

• A.M A
• nth term B
• Central term C
• None of these 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

• 
  A
• 
  B
• 
  C
• 
  D

• 15/23 A
• 7/15 B
• 7/8 C
• 15/7 D

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

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

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

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

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

A number A is said to be the A.M between the two numbers a and b if a, A, b are in

• A.M A
• A.P B
• G.P C
• G.M D

A sequence having no last term is called

• arithmetic sequence A
• Geometric sequence B
• Finite sequence C
• Infinite sequence 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 nth term of an A.P is (3n+5) Its 75th term is

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

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

• 136 A
• -136 B
• 148 C
• -148 D

How many term are there in the A.P, in which a₁ = 11 , a_n =68, d=3

• 30 A
• 27 B
• 20 C
• 21 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 function whose domain is a subset of natural numbers is called ______

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

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

• 1st term A
• General term B
• Last term 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

The sum of an indicated number of terms in a sequence is called

• sequence A
• progression B
• Series C
• Mean D