MCQs On Arithmetic Progression

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Arithmetic Progression (AP) is a numerical series in which the difference between any two subsequent integers is a fixed value. Arithmetic Sequence is another name for Arithmetic Progression. For instance, the natural number sequence 1, 2, 3, 4, 5, 6, is an Arithmetic Progression with a common difference of 1 between two subsequent terms (say 1 and 2). (2 -1). Even when dealing with odd and even numbers, the common difference between two consecutive words will be equal to 2.

Ques: Find the sum of the first 5 terms of the AP: 10, 6, 2…

–320
512
10
–960

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Arithmetic Progression Detailed Video Explanation:

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Ans: (c) 10

Explanation: AP: 10, 6, 2, …

a = 10, d = - 4

Sum of first n terms = S(n) = (n/2) x [2a + (n – 1) x d]

S5 = (5/2) x [2 x (10) + (5 – 1) x (-4)]

= (5/2) x [20 + 4 x (-4)]

= (5/2) x (20 – 16)

= (5/2) x (4)

= 5 x 2

= 10

Ques: The d for the series of numbers -12, –6, 0, 6… is

–2
6
8
-1

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Ans: (b) 6

Explanation:

–12, –6, 0, 6,…

Let a(1) = -12, a(2) = -6, a(3) = 0, a(4) = 6

First relational d,

a(2) – a(1) = -6 – (-12) = 6

Second relational d,

a(3) – a(2) = 0 – (-6) = 6

Third relational d,

a(4) – a(3) = 6 – (0) = 6

all the d are equals to each other, hence

d = 6.

Ques: Find the number of multiples of 4 falling between 10 and 250 is:

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Ans: (c) 60

Explanation: 4’s multiples are:

12, 16, 20, 24, …

a = 12 and d = 4

2 is the remainder for 250 / 4.

250 – 2 = 248 which is divisible by 2.

12, 16…248

nth term, a(n) = 248

a(n) = a + (n − 1) x d

248 = 12 + (n-1) × 4

236 / 4 = n - 1

59 = n - 1

n = 60

Ques. In the A.P. -3, -1/2, 2 …. The 11th term is

42
-12
22
65

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Ans: (c) 22

Explanation: The A.P. is -3, -1/2, 2 …

Where a = – 3

d = a(2) – a(1) = (-1 / 2) - (-3)

⇒ (-1 / 2) + 3 = 5 / 2

a(n) = a + (n−1) x d

a(11) = 3 + (11-1) x (5 / 2)

a(11) = 3 + (10) x (5 / 2)

a(11) = -3 + 25

a(11) = 22

Ques: The name of the famous mathematician who is credited with discovering the total value of the very first 100 natural numbers is

Gauss
Pythagoras
Euclid
Newton

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Ans: (a) Gauss

Explanation: Gauss is the great mathematician who is credited with discovering the total value of the first 100 natural numbers.

Ques: For a given AP, a(n) = 4, n = 7, d = -4, find the value of a

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Ans: (d) 28

Explanation: d = -4, n = 7, a(n) = 4

a(n) = a + (n – 1) x d

a + (7 – 1) x (-4) = 4

a + 6 x (-4) = 4

a – 24 = 4

a = 4 + 24

a = 28

Ques: If a(17) exceeds it’s a(10) by 7. The d is:

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Ans: (c) 1

Explanation: for a given AP, the Nth term is:

a(n) = a + (n-1) x d

a(17) = a + (17−1) x d

a(17) = a + 16 x d

a(10) = a+9(d)

a(17) – a(10) = 7

(a + 16 x d) − (a + 9 x d) = 7

7 x d = 7

d = 1

Ques: 10, 7, 4, …, is an AP, what will be the 30th term of this series?

65
22
-77
45

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Ans: (c) -77

Explanation: A.P. given in the question is 10, 7, 4, …

a = 10

d = a(2) – a(1) = 7 − 10 = −3

a(n) = a + (n−1) x d

a(30) = 10 + (30−1) x (−3)

a(30) = 10 + (29) x (−3)

a(30) = 10 − 87 = −77

Ques: What is the d of an AP in which a(18) – a(14) = 32?

-6
1
5
8

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Ans: (d) 8

Explanation:

a(18) – a(14) = 32

a(n) = a + (n – 1) x d

a + (17) x d – (a + 13 x d) = 32

(17) x d – (13) x d = 32

(4) x d = 32

d = 8

Ques: 5, 8, 11, 14, … is an AP, what will be the a(10)?

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Ans: (c) 32

Explanation:

The given series : 5, 8, 11, 14, …

a = 5

d = 8 – 5 = 3

a(n) = a + (n – 1) x d

10th term = a(10) = a + (10 – 1) x d

= 5 + 9 x (3)

= 5 + 27

= 32

Ques: a and a(2) are -3 and 4, find the a(21) of the series.

26
95
137
-43

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Ans: (c) 137

Explanation: a = -3 and a(2) = 4

a = -3

d = 4 - a = 4 - (-3) = 7

a(21)=a + (21-1) x d

= -3 + (20) x 7

= -3 + 140

= 137

Ques: For this given AP 3, 1, -1, -3, find the values of a and d is:

3, -2
0, 3
1, 2
-2, 3

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Ans: (a) 3 and -2

Explanation: a = 3

d = a(2) – a(1)

⇒ 1 – 3 = -2

⇒ d = -2

Ques: Does 210 falls in the AP: 21, 42, 63, 84…? If yes, then on which term?

12^th
10^th
5^th
7th

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Ans: (b) 10th

Explanation:

AP: 21, 42, 63, 84, …

a = 21

d = 42 – 21 = 21

a(n) = 210

a + (n – 1) x d = 210

21 + (n – 1) x (21) = 210

21 + 21 x n – 21 = 210

21 x n = 210

n = 10

Ques: The total value of the starting four multiples of 2 is:

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Ans: (a) 20

Explanation: The starting four multiples of 2 is 2, 4, 6, 8

a=2 and d=2

n=4

S(n) = (n / 2) x [2a + (n - 1) x d]

S(4) = (4 / 2) x [2 x (2) + (4 - 1) x 2]

= (2) x [4 + 6]

= (2) x [10]

= 20

Ques: On which number of term does 78 falls in the A.P. 3, 8, 13, 18, … is 78?

9^th
20^th
16^th
4th

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Ans: (c) 16th

Explanation: Given, 3, 8, 13, 18, … is the AP.

a = 3

d = a(2) – a(1) = 8 − 3 = 5

Let a(n) term be 78.

a(n) = a + (n − 1) x d

78 = 3 + (n − 1) x 5

75 = (n − 1) x 5

(n − 1) = 15

n = 16

Ques: The first four terms of an AP whose a is 10 and d is 10 will be?

12, 24, 36, 48
8, 16, 24, 32
15, 30, 45, 60
10, 20, 30, 40

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Ans: (d) 10, 20, 30, 40

Explanation: a = 10, d = 10

a(1) = a = 10

a(2) = a1 + d = 10 + 10 = 20

a(3) = a2 + d = 20 + 10 = 30

a(4) = a3 + d = 30 + 10 = 40

Ques: In an AP, if d = -4, a = 28, n = 7, then an is:

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Ans: (c) 4

Explanation:

a(n) = a + (n - 1) x d

= 28 + (7 - 1) x (-4)

= 28 + 6 x (-4)

= 28 - 24

a(n) = 4

Ques: The missing terms in AP: __, 13, __, 3 are:

25, 5
15, 9
19, 7
18, 8

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Ans: (d)

Explanation: a² = 13 and

a(4) = 3

The nth term of an AP;

a(n) = a + (n − 1) x d

a(2) = a + (2 - 1) x d

13 = a + d ………………. (i)

a(4) = a + (4 - 1) x d

3 = a + 3d ………….. (ii)

Subtracting equation (i) from (ii), we get

– 10 = 2 x d

d = – 5

put value of d in eq 1

13 = a + (-5)

a = 18

a(3) = 18 + (3 - 1) x (-5)

= 18 + 2 x (-5)

= 18 - 10 = 8

Ques: Starting from the last, the 20th term of the A.P. 3, 8, 13, …, 253 is:

131
123
137
158

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Ans: (d) 158

Explanation: A.P. is 3, 8, 13, …, 253

d= 5.

Starting from the end of the series,

253, 248, 243, …, 13, 8, 5

a = 253

d = 248 − 253 = −5

n = 20

a(20) = a + (20 − 1) x d

a(20) = 253 + (19) x (−5)

a(20) = 253 − 95

a(20) = 158

Ques: If the a(2) is 13 and a(5) is 25, then it’s a(7) is

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Ans: (d) 33

Explanation:

a(2) = 13

a + d = 13

a = 13 – d…. (i)

a(5) = 25

a + 4d = 25….(ii)

Substituting the value of (i) in (ii),

13 – d + 4 x d = 25

3 x d = 12

d = 4

So, a = 13 – 4 = 9

a(7) = a + 6d = 9 + 6(4) = 9 + 24 = 33

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MCQs On Arithmetic Progression

Arithmetic Progression Detailed Video Explanation:

CBSE X Related Questions

1.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

2.
The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

3.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

4.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

5.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

6.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

Similar Mathematics Concepts

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MCQs On Arithmetic Progression

Arithmetic Progression Detailed Video Explanation:

CBSE X Related Questions

1.Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

2.The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

3.The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

4.Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

5.Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

6.Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent. Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

2.
The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

3.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

4.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

5.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

6.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.