 # Class 10 Maths Chapter 5 Arithmetic Progression MCQs

Class 10 Maths MCQs for Chapter 5 (Arithmetic Progression) is made available online here for students to score better marks in exams. These objective questions are provided here with answers and detailed explanations as per the CBSE syllabus and NCERT guidelines. The chapter-wise multiple choice questions for Class 10 Maths are given here.

## Class 10 Maths MCQs for Arithmetic Progressions

Students of 10th standard can practice these questions to develop their problem-solving skills and increase their confidence level. The Arithmetic progression chapter teaches us about the arrangement of numbers or objects in Maths and in real-life situations. It has huge applications. Get important questions for class 10 Maths here as well.

Students can also get access to Arithmetic Progression Class 10 Notes here.

#### Below are the MCQs for Arithmetic Progression

1. In an Arithmetic Progression, if a = 28, d = -4, n = 7, then an is:

(a) 4

(b) 5

(c) 3

(d) 7

Explanation: For an AP,

an = a+(n-1)d

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

= 28+6(-4)

= 28-24

an=4

2. If a = 10 and d = 10, then first four terms will be:

(a) 10, 30, 50, 60

(b) 10, 20, 30, 40

(c) 10, 15, 20, 25

(d) 10, 18, 20, 30

Answer: (b) 10, 20, 30, 40

Explanation: a = 10, d = 10

a1 = a = 10

a2 = a1+d = 10+10 = 20

a3 = a2+d = 20+10 = 30

a4 = a3+d = 30+10 = 40

3. The first term and common difference for the A.P. 3, 1, -1, -3 is:

(a) 1 and 3

(b) -1 and 3

(c) 3 and -2

(d) 2 and 3

Explanation: First term, a = 3

Common difference, d = Second term – First term

⇒ 1 – 3 = -2

⇒ d = -2

4. 30th term of the A.P: 10, 7, 4, …, is

(a) 97

(b) 77

(c) -77

(d) -87

Explanation: Given,

A.P. = 10, 7, 4, …

First term, a = 10

Common difference, d = a2 − a1 = 7−10 = −3

As we know, for an A.P.,

an = a +(n−1)d

Putting the values;

a30 = 10+(30−1)(−3)

a30 = 10+(29)(−3)

a30 = 10−87 = −77

5. 11th term of the A.P. -3, -1/2, 2 …. Is

(a) 28

(b) 22

(c) -38

(d) -48

Explanation: A.P. = -3, -1/2, 2 …

First term a = – 3

Common difference, d = a2 − a1 = (-1/2) -(-3)

⇒(-1/2) + 3 = 5/2

Nth term;

an = a+(n−1)d

a11 = 3+(11-1)(5/2)

a11 = 3+(10)(5/2)

a11 = -3+25

a11 = 22

6. The missing terms in AP: __, 13, __, 3 are:

(a) 11 and 9

(b) 17 and 9

(c) 18 and 8

(d) 18 and 9

Explanation: a2 = 13 and

a4 = 3

The nth term of an AP;

an = a+(n−1) d

a2 = a +(2-1)d

13 = a+d ………………. (i)

a4 = a+(4-1)d

3 = a+3d ………….. (ii)

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

– 10 = 2d

d = – 5

Now put value of d in equation 1

13 = a+(-5)

a = 18 (first term)

a3 = 18+(3-1)(-5)

= 18+2(-5) = 18-10 = 8 (third term).

7. Which term of the A.P. 3, 8, 13, 18, … is 78?

(a) 12th

(b) 13th

(c) 15th

(d) 16th

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

First term, a = 3

Common difference, d = a2 − a1 = 8 − 3 = 5

Let the nth term of given A.P. be 78. Now as we know,

an = a+(n−1)d

Therefore,

78 = 3+(n −1)5

75 = (n−1)5

(n−1) = 15

n = 16

8. The 21st term of AP whose first two terms are -3 and 4 is:

(a) 17

(b) 137

(c) 143

(d) -143

Explanation: First term = -3 and second term = 4

a = -3

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

a21=a+(21-1)d

=-3+(20)7

=-3+140

=137

9. If 17th term of an A.P. exceeds its 10th term by 7. The common difference is:

(a) 1

(b) 2

(c) 3

(d) 4

Explanation: Nth term in AP is:

an = a+(n-1)d

a17 = a+(17−1)d

a17 = a +16d

In the same way,

a10 = a+9d

Given,

a17 − a10 = 7

Therefore,

(a +16d)−(a+9d) = 7

7d = 7

d = 1

Therefore, the common difference is 1.

10. The number of multiples of 4 between 10 and 250 is:

(a) 50

(b) 40

(c) 60

(d) 30

Explanation: The multiples of 4 after 10 are:

12, 16, 20, 24, …

So here, a = 12 and d = 4

Now, 250/4 gives remainder 2. Hence, 250 – 2 = 248 is divisible by 2.

12, 16, 20, 24, …, 248

So, nth term, an = 248

As we know,

an = a+(n−1)d

248 = 12+(n-1)×4

236/4 = n-1

59 = n-1

n = 60

11. 20th term from the last term of the A.P. 3, 8, 13, …, 253 is:

(a) 147

(b) 151

(c) 154

(d) 158

Explanation: Given, A.P. is 3, 8, 13, …, 253

Common difference, d= 5.

In reverse order,

253, 248, 243, …, 13, 8, 5

So,

a = 253

d = 248 − 253 = −5

n = 20

By nth term formula,

a20 = a+(20−1)d

a20 = 253+(19)(−5)

a20 = 253−95

a20 = 158

12. The sum of the first five multiples of 3 is:

(a) 45

(b) 55

(c) 65

(d) 75

Explanation: The first five multiples of 3 is 3, 6, 9, 12 and 15

a=3 and d=3

n=5

Sum, Sn = n/2[2a+(n-1)d]

S5 = 5/2[2(3)+(5-1)3]

=5/2[6+12]

=5/2

=5 x 9

= 45

13. The 10th term of the AP: 5, 8, 11, 14, … is

(a) 32

(b) 35

(c) 38

(d) 185

Explanation:

Given AP: 5, 8, 11, 14,….

First term = a = 5

Common difference = d = 8 – 5 = 3

nth term of an AP = an = a + (n – 1)d

Now, 10th term = a10 = a + (10 – 1)d

= 5 + 9(3)

= 5 + 27

= 32

14. In an AP, if d = -4, n = 7, an = 4, then a is

(a) 6

(b) 7

(c) 20

(d) 28

Solution;

Given,

d = -4, n = 7, an = 4

We know that,

an = a + (n – 1)d

4 = a + (7 – 1)(-4)

4 = a + 6(-4)

4 = a – 24

⇒ a = 4 + 24 = 28

15. The list of numbers –10, –6, –2, 2,… is

(a) an AP with d = –16

(b) an AP with d = 4

(c) an AP with d = –4

(d) not an AP

Answer: (b) an AP with d = 4

Explanation:

–10, –6, –2, 2,…

Let a1 = -10, a2 = -6, a3 = -3, a4 = 2

a2 – a1 = -6 – (-10) = 4

a3 – a2 = -2 – (-6) = 4

a4 – a3 = 2 – (-2) = 4

The given list of numbers is an AP with d = 4.

16. If the 2nd term of an AP is 13 and the 5th term is 25, then its 7th term is

(a) 30

(b) 33

(c) 37

(d) 38

Explanation:

Given,

a2 = 13

a + d = 13

a = 13 – d….(i)

a5 = 25

a + 4d = 25….(ii)

Substituting (i) in (ii),

13 – d + 4d = 25

3d = 12

d = 4

So, a = 13 – 4 = 9

a7 = a + 6d = 9 + 6(4) = 9 + 24 = 33

17. Which term of the AP: 21, 42, 63, 84,… is 210?

(a) 9th

(b) 10th

(c) 11th

(d) 12th

Explanation:

Given AP:

21, 42, 63, 84,…

a = 21

d = 42 – 21 = 21

an = 210

a + (n – 1)d = 210

21 + (n – 1)(21) = 210

21 + 21n – 21 = 210

21n = 210

n = 10

18. What is the common difference of an AP in which a18 – a14 = 32?

(a) 8

(b) -8

(c) -4

(d) 4

Explanation:

Given,

a18 – a14 = 32

We know that, an = a + (n – 1)d

So,

a + 17d – (a + 13d) = 32

17d – 13d = 32

4d = 32

d = 8

19. The famous mathematician associated with finding the sum of the first 100 natural numbers is

(a) Pythagoras

(b) Newton

(c) Gauss

(d) Euclid

Explanation:

The famous mathematician associated with finding the sum of the first 100 natural numbers is Gauss.

20. The sum of first 16 terms of the AP: 10, 6, 2,… is

(a) –320

(b) 320

(c) –352

(d) –400

Explanation:

Given AP: 10, 6, 2,…

Here, a = 10, d = -4

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

The sum of first 16 terms = S16 = (16/2)[2(10) + (16 – 1)(-4)]

= 8[20 + 15(-4)]

= 8(20 – 60)

= 8(-40)

= -320