Sequences and Series Test

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Sequences and Series Test - 6

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Weekly Quiz Competition

Question 1
2 / -0.83

If the numbers a, b, c, d, e form an A.P. then the value of a –4b + 6c –4d + e is

A
0

B
2

C
1

D
none of these
Question 2
2 / -0.83

The sum of all non-reducible fractions with the denominator 3 lying between the numbers 5 and 8 is

A
39

B
31

C
41

D
52
Question 3
2 / -0.83

The next term of the sequence 1, 1, 2, 4, 7, 13,…. Is

A
19

B
21

C
24

D
none of these
Question 4
2 / -0.83

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

A
mn

B
mn²

C
1/2 mn

D
2 mn
Question 5
2 / -0.83

The terms equidistant from a given term of an A.P. are multiplied together, then the difference of the successive terms of the series so formed are in

A
A.P.

B
H.P.

C
G.P.

D
equal
Question 6
2 / -0.83

If the numbers a, b, c are in A.P., b, c, d are in G.P. and c, d , e are in H.P., then a, c, e are in

A
H.P.

B
G.P.

C
A.P.

D
none of these
Question 7
2 / -0.83

If x, y, z are in A.P., then (x + 2y –z) (x + z –y) (z + 2y –x) is equal to

A
4xyz

B
2xyz

C
xyz

D
none of these
Question 8
2 / -0.83

If a, b , c are in A.P. and also 1/a, 1/b, 1/c are A. P., then

A
a = b ≠c

B
a = b = c

C
a ≠b ≠c

D
a ≠b = c
Question 9
2 / -0.83

The sum of terms equidistant from the beginning and end in A.P. is equal to

A
sum of the first and the last terms

B
last term

C
first term

D
none of these
Question 10
2 / -0.83

Sum of first 5 terms of an A.P. is one fourth of the sum of next five terms. If the first term = 2, then the common difference of the A.P. is

A
3

B
6

C
- 6

D
none of these
Question 11
2 / -0.83

The first, second and last terms of an A.P. are a, b and 2 a. The number of terms in the A.P. is

A
b/b+a

B
a/b+a

C
b/b-a

D
a/b-a
Question 12
2 / -0.83

The sum of all the two-digit numbers is

A
4905

B
4895

C
1605

D
none of these
Question 13
2 / -0.83

Sum of all 2 digit odd numbers is

A
2530

B
5049

C
2475

D
4905

Solution

All two-digit odd positive numbers are 11, 13, 15, 17, ...., 99. which are in AP with a=11,d=2,l = 99
Let the number of terms be n.
an=99
a+(n −1)d=99
11+(n −1)×2=99
n=45
Sum of n terms is given by Sn= n/2(a+l)
Sn= 45/2(11+99) = 2475
Question 14
2 / -0.83

The number of terms common to the two A.P.s 2 + 5 + 8 + 11 + …+ 98 and 3 + 8+ 13 + 18+ 23 + …+ 198

A
7

B
33

C
40

D
none of these

Solution

For first A.P 2+5+8+11+......+98
a=2,an=98,d=3
an=a+(n −1)d
98=2+(n −1)3
98=2+3n −3
3n=99
n=33
Number of term =33
For first A.P 3+8+13+18+......+198
a=3,an=198,d=5
an=a+(n −1)d
198=3+(n −1)5
198=3+5n −5
5n=200
n=40
No of terms =40
Common terms=40 −33=7
Question 15
2 / -0.83

The values of x for which the solutions of the equation cos θ= x, θ≥0 form an A.P. are

A
0 and 1

B
- 1 and 1

C
0, 1 and –1

D
none of these

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Sequences and Series Test - 6

Result

Sequences and Series Test - 6

Score

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Rank

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SHARING IS CARING

Question 1

0

2

1

none of these

Question 2

39

31

41

52

Question 3

19

21

24

none of these

Question 4

mn

mn2

1/2 mn

2 mn

Question 5

A.P.

H.P.

G.P.

equal

Question 6

H.P.

G.P.

A.P.

none of these

Question 7

4xyz

2xyz

xyz

none of these

Question 8

a = b ≠c

a = b = c

a ≠b ≠c

a ≠b = c

Question 9

sum of the first and the last terms

last term

first term

none of these

Question 10

3

6

- 6

none of these

Question 11

b/b+a

a/b+a

b/b-a

a/b-a

Question 12

4905

4895

1605

none of these

Question 13

2530

5049

2475

4905

Solution

Question 14

7

33

40

none of these

Solution

mn²