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

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 sum of first 60 natural numbers is

• 1830 A
• 3660 B
• 1640 C
• 1770 D

• 
  A
• 
  B
• 
  C
• 
  D

• 1 A
• 2 B
• 3/2 C
• 5/2 D

An infinite arithmetic series is always

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

H.M. between 3 and 7 is

• 
  A
• 
  B
• 
  C
• 
  D

A sequence whose reciprocal is an A.P is called

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

Arithmetic mean between x - 3 and x + 5 is

• x + 1 A
• x + 2 B
• x + 3 C
• x + 4 D

Find the geometric mean between 4 and 16

• 
  A
• 
  B
• 
  C
• 
  D

An indicated sum of terms of a sequence is represented by

• Sn A
• an B
• S(n) C
• {Sn} 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

The element range of sequence are called

• Series A
• progression B
• Members C
• Terms 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

No term of a geometric sequence can be

• 0 A
• 1 B
• 2 C
• 3 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

The 10th common term between the series 3+7+11+....... and 1 + 6 +11 + ....... is

• 191 A
• 193 B
• 211 C
• None of these D

The third term of the sequence a_n= (-1)^n-1(n-7) is ______

• 8 A
• 4 B
• -4 C
• 8 D

An A.P. consists of n(odd terms) and its middle term is m. then the sum of the A.P. is

• 2 mn A
• 1/2 mn B
• mn C
• mn² 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

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

Let a₁, a₂, a₃, a₄and a₅be such that a₁, a₂, and a₃are in A.P., a₂, a₃and a₄are in G.P and a₃, a₄and a₅are in H.P. Then, a₁, a₃and a₅are in

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

The sum of all 2 digit number is

• 4750 A
• 3776 B
• 4895 C
• 4905 D

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

• 400 A
• 397 B
• 404 C
• 408 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

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

• 
  A
• 
  B
• 
  C
• 
  D

If p, q, r and in A.P., a is G.M. between p and q and b is G.M. between q and r, then a², q², b²are in

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

5th term of a G.P. is 2, then the product of first 9 terms is

• 256 A
• 128 B
• 512 C
• None of these D

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