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

The general term of a sequence is denoted by

• a₁ A
• a_n B
• n C
• s_n D

• 
  A
• 
  B
• 
  C
• 
  D

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

• 54 A
• 12 B
• 4 C
• 9 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

What is the 26th term of the sequence, if its general term is a_{n = (-1)}ⁿ⁺¹

• 2 A
• 26 B
• 27 C
• 1 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

The seventh term of an A.P whose first term is P and common difference is q. is

• P-6q A
• P+6q B
• P-4q C
• P-nq D

an -an-1,∀n∈N∧n>1 in an A.P is called

• Common difference A
• nth term B
• Common ratio C
• None of these 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

• 12 A
• 13 B
• 14 C
• 15 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

The 7th term of the A.P 7,11,15,is

• 24 A
• 31 B
• 26 C
• 23 D

If the pth, qth, and rth terms of an A.P. are in G.P:., then the common ratio of the G.P. is

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

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

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 sixth term of the sequence 1,3,12,60....is

• 1500 A
• 72 B
• 2160 C
• 2520 D

The series obtained by adding the terms of a geometric sequence is called

• Infinite series A
• Arithmetic series B
• Geometric series C
• Harmonic series D

The 6th term of the sequence 7,9,12,16......is

• 27 A
• 32 B
• 20 C
• 19 D

• 
  A
• 
  B
• 
  C
• 
  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

An infinite sequence has no

• nth term A
• Last term B
• Sum C
• None of these 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 A.P common difference d

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

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

• 1 A
• 0 B
• -1 C
• -2 D

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

• 136 A
• -136 B
• 148 C
• -148 D

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

• 
  A
• 
  B
• 
  C
• 
  D