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

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 infinite geometric series exist if

• | r | < 1 A
• | r | > 1 B
• r = 1 C
• r = -1 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
• 
  B
• 
  C
• 
  D

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

• 136 A
• -136 B
• 148 C
• -148 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

The common ration of a geometric sequence cannot be

• 0 A
• 1 B
• 2 C
• 3 D

Arithmetic mean between a and b is

• 
  A
• 
  B
• 
  C
• 
  D

If a₁, r are first term and the common ratio respectively then the sum of an infinite geometric series is

• 
  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

The three consecutive numbers a,√ab,b are in

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

• 0 A
• 1 B
• 2 C
• 3 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

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 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

• 1 A
• 2 B
• 3/2 C
• 5/2 D

The sum of first twenty odd integers in A.P is

• 400 A
• 397 B
• 404 C
• 408 D

An A.P., a G.P. and a H.P. have the same first and last terms and the same odd numbers of terms, the middle terms of the three series are in

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

• 12 A
• 13 B
• 14 C
• 15 D

A sequence having no last term is called

• arithmetic sequence A
• Geometric sequence B
• Finite sequence C
• Infinite sequence D

Geometric mean between a and b is

• 
  A
• 
  B
• 
  C
• 
  D

1 + 2 + 3 + ...... + n = ______

• 
  A
• 
  B
• 
  C
• 
  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

A sequence is a functions whose domain is a subset of the set of

• Natural numbers A
• Real numbers B
• Whole numbers C
• Rational numbers 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

The third term of a G.P. is the square of first term. If the second term is 8, then the 6th term is

• 120 A
• 124 B
• 128 C
• 132 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

if a_{9 =19,a9=31 are the 6th and 9th term of an A.P. and d=4 is the common difference, then 18th term of the sequence is}

• 65 A
• 67 B
• 71 C
• 75 D

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