MCQs On Arithmetic Progression

Education Journalist | Study Abroad Strategy Lead

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

The video below explains this:

Arithmetic Progression Detailed Video Explanation:

Click here for the answer

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

Click here for the answer

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:

Click here for the answer

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

Click here for the answer

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

Click here for the answer

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

Click here for the answer

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:

Click here for the answer

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

Click here for the answer

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

Click here for the answer

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)?

Click here for the answer

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

Click here for the answer

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

Click here for the answer

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

Click here for the answer

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:

Click here for the answer

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

Click here for the answer

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

Click here for the answer

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:

Click here for the answer

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

Click here for the answer

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

Click here for the answer

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

Click here for the answer

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

Read Also:

Permutations and Combinations	Trigonometry	Geometric Mean (G.M.)
Remainder Theorem	Arithmetic Progression (A.P.)	Real Numbers Formula
Complex Numbers and Quadratic Equations	Polynomials Important Questions	Rolle’s Theorem
Real Numbers	Bayes Theorem Formula	Mean Value Theorem

MCQs On Arithmetic Progression

Arithmetic Progression Detailed Video Explanation:

CBSE X Related Questions

1.
PQ is tangent to the circle with centre O such that OP = 2OQ. m\(\angle\)OPQ is

2.
In the given figure, \(\Delta ABC\) is a right-angled triangle with \(\angle A = 90^\circ\). AD is perpendicular to BC.

35(a)(i) Prove that \(\Delta DBA \sim \Delta DAC\)

3.
Find the missing frequencies p and q in the following frequency distribution, when sum of frequencies is 40 and mean is 19 :

5.
\(17 \times 11 \times 13 + 11\) is

6.
Determine the ratio in which the line \(2x + y = 6\) divides the line segment joining the points (1, 3) and (2, 5).

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

MCQs On Arithmetic Progression

Arithmetic Progression Detailed Video Explanation:

CBSE X Related Questions

1.PQ is tangent to the circle with centre O such that OP = 2OQ. m\(\angle\)OPQ is

2.In the given figure, \(\Delta ABC\) is a right-angled triangle with \(\angle A = 90^\circ\). AD is perpendicular to BC. 35(a)(i) Prove that \(\Delta DBA \sim \Delta DAC\)

3.Find the missing frequencies p and q in the following frequency distribution, when sum of frequencies is 40 and mean is 19 :

5.\(17 \times 11 \times 13 + 11\) is

6.Determine the ratio in which the line \(2x + y = 6\) divides the line segment joining the points (1, 3) and (2, 5).

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
PQ is tangent to the circle with centre O such that OP = 2OQ. m\(\angle\)OPQ is

2.
In the given figure, \(\Delta ABC\) is a right-angled triangle with \(\angle A = 90^\circ\). AD is perpendicular to BC.

35(a)(i) Prove that \(\Delta DBA \sim \Delta DAC\)

3.
Find the missing frequencies p and q in the following frequency distribution, when sum of frequencies is 40 and mean is 19 :

5.
\(17 \times 11 \times 13 + 11\) is

6.
Determine the ratio in which the line \(2x + y = 6\) divides the line segment joining the points (1, 3) and (2, 5).