Chapter 6: SEQUENCES AND SERIES
1)
The general term of the sequence 2/1, 3/2, 4/3,
…. is an =
n+1
A) n n
B) n+1 n
C) n−1
n−1
D) n
Answer: A
2)
If a, a+d, a+2d, …… is A.P, then an =
A) a
+ nd
B) a
– nd
C) a
+ (n – 1)d
D) a
+ (n + 1)d
Answer: C
an+1 +bn+1
3)
n n is arithmetic mean between a and b
if n = a +b
A) –1
B) 1
C)
0
D) 2
Answer: C
4)
If A,. G, H are A.M, G.M, and H.M between
numbers, then
A) A
< G < H
B) A
< G > H C) A > G > H
D) A > G < H
Answer: C
5)
The harmonic mean between two numbers a and b is
A) ± ab a+b
B)
2
2ab
C)
a+b
2ab
D)
a−b
Answer: C
6)
The arithmetic mean between 4 and 6 is
A)
24 
B)
− 24 
C)
24/5
D)
5
Answer: D
7)
If a is the first term and r < 1 is common
ratio of G.P, then Sn =
a(1−rn)
A)
1−r
a(1+rn)
B)
1+r
C) arn
a(1−rn)
D)
1+r Answer:
A
8)
An infinite geometric series is convergent if
A) r <1
B)
r > 1
C)
r = 1
D)
Both B and C are correct
Answer: A
9)
If a is the first term and r is the common
ration of G.P then an =
B) arn+1
two a(1−rn)
C)
1−r
a(1+rn)
D)
1+r Answer:
A
an+1 +bn+1
10)
n n is H.M between a and b if a +b
A)
n = 0
B)
n = 1
C)
n = -1
D)
n = 2
Answer: C
11)
If a is the first term and r is common ratio
such that r < 1, then S∝
=
a
A)
1−r a
B)
a(1−rn)
C)
1−r
a(1+rn)
D)
1+r Answer:
A
12)
The harmonic mean between 9 and 11 is
A) 10
B) ± 99
C) − 99
D) 99/10
Answer: D
13)
If A, G, H are arithmetic mean, geometric and
harmonic mean between a and b, then
A) G2
= AH B) A2 = GH
C) H2 = AG D) None
of these
Answer: A
14)
-1, 1, -1, 1, …. is
A) Arithmetic
Sequence
B) Geometric
Sequence
C) Alternating
Sequence
D) Harmonic
Sequence
Answer: C
15)
The geometric mean between 8/9, 9/8 is
A) +
1
B) –
1
C) ± 1
Answer: C
16)
A sequence is a function whose domain is
A) the
set of rational numbers B) The set of irrational numbers
C) The
set of integers
D) The
set of natural numbers
Answer: D
17)
The geometric mean between a and b is
a+b
D)
2ab
Answer: B
18)
The arithmetic mean between a and b is
2ab
A) a+b
a+b
B)
2ab a+b
C)
D) ± ab 
Answer: C
19)
Which of the following series is
convergent.
A) 2
– 6 + 18 - …… B) 8 + 4 + 2 + …….
C) 5 + 10 + 20 + ……. D) 3/2
+ 3 + 6 + ……..
Answer: B
20)
If a = 3, r = 2/3, then sum of infinite S∝ =
A) 9
B) 
C) 
D) 
Answer: A
21)
If 2 + 1 + ½ + ….. is infinite geometric series
then S∝
|
A) 2
B) 4
C) ½
D) ¼
|
|
|
Answer:
|
B
|
22)
The population of a town increases geometrically
at the rate of 4% per year. If the present population is
100,000, then population after 4
years will be
A) 100,000
(1 + .04)3 B) 100,000 (1 + .04)4
C) 100,000
(1 – 0.04)3
D) 100,000
(1 – 0.04)4
Answer: B
23)
The sum of n terms of arithmetic series Sn
=
A) n/2[2a
+ (n – 1)d]
B) arn – 1
a(1−rn)
C)
 |
1−r
D) a + (n – 1)d
Answer: A
24)
The two arithmetic means between 5 and 35 are
A) 15,
25 B) 10, 20 C) 10, 15
D) 10, 25
Answer: A
25)
If 2b – 1, 4b + 1, 15b – 3 is a geometric
sequence, then b =
|
A) 4 B) 3 C) 2
D) 1
|
|
|
Answer:
|
C
|
26)
Which of the following is a geometric series?
A) 5,
7, 9, 11, …..
B) 3,
5, 7, 9…….
C) 1,
1/3, 3, 9, …..
D) 9,
3, 1, 1/3, ……
Answer: D
27)
The general term of the sequence 3, 6, 9, 12 …..
is
A) n
B)
2n
C)
3n
D)
n2 Answer: C
28)
Which of the following is harmonic
sequence?
A) 3,
5, 7 …… B) ½, ¼, 1/8, …..
C) ½,
1/3, ¼ ……
D) 3,
9, 27 …..
Answer: C
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