__Mathematics__

__Multiple Choice Questions (MCQ)__

MCQ | Class 10 | Chapter 5

__ARITHMATIC PROGRESSION__

**MCQ Based on the general Arithmetic Progression.****MCQ Based on the nth term of Arithmetic Progression.****MCQ Based on the sum of n terms of Arithmetic Progression.****MCQ Based on the word problems of Arithmetic Progression.****MCQ Based from the nth term from the end of the sequence.**

__Features__

**In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. ****Solution Hints are also given to some difficult problems. ****Each MCQ contains four options from which one option is correct. ****On the right hand side column of the pdf Answer option is given.**

__Action Plan__

**First of all students should Learn and write all basic points and Formulas related to the Arithmetic Progression.****Start solving the NCERT Problems with examples.****Solve the important assignments on the Arithmetic Progression.****Then start solving the following MCQ.**

**MCQ | CHAPTER 5 | CLASS 10**

**ARITHMETIC PROGRESSION**

Q 1) In an Arithmetic Progression, if a = 28, d = - 4, n = 7, then

a_{n} is:

a) 4

b) 5

c) 3

d) 7

Ans: a

Q 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

Ans: b

Q 3) 30th term of the A.P: 10, 7, 4, …, is

a) 97

b) 77

c) - 77

d) - 87

Ans: c

Q 4) 11th term of the A.P. - 3, -1/2, 2 …. Is

a) 28

b) 22

c) – 38

d) – 48

Ans: b

Q 5) The missing terms in AP: __, 13, __, 3 are:

a) 11 and 9

b) 17 and 9

c) 18 and 8

d) 18 and 9

Ans: c

Q 6) Which term of the A.P. 3, 8, 13, 18, … is 78?

a) 12th

b) 13th

c) 15th

d) 16th

Ans: d

Q 7) The 21st term of AP whose first two terms are -3 and 4 is:

a) 17

b) 137

c) 143

d) -143

Ans: b

Q 8) The number of multiples of 4 between 10 and 250 is:

a) 50

b) 40

c) 60

d) 30

Ans: c

Q 9) 20th term from the last term of the A.P. 3, 8, 13, …, 253 is:

a) 147

b) 151

c) 154

d) 158

Ans: d

Q 10) The sum of the first five multiples of 3 is:

a) 45

b) 55

c) 65

d) 75

Ans: a

Q 11) In an AP, if d = - 4, n = 7, a_{n} = 4, then a is

a) 6

b) 7

c) 20

d) 28

Ans: d

Q 12) 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

Ans: b

Q 13) 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

Ans: b

Q 14) Which term of the AP: 21, 42, 63, 84,… is 210?

a) 9th

b) 10th

c) 11th

d) 12th

Ans: b

Q 15) What is the common difference of an AP in which a_{18} – a_{14} = 32?

a) 8

b) – 8

c) – 4

d) 4

Ans: a

Q 16) The famous mathematician associated with finding the sum of the first 100 natural numbers is

a) Pythagoras

b) Newton

c) Gauss

d) Euclid

Ans: c

Q 17) The sum of first 16 terms of the AP: 10, 6, 2,… is

a) –320

b) 320

c) –352

d) –400

Ans: a

Q 18) The nth term of an A.P. is given by an = 3 + 4n. The common difference is

a) 7

b) 3

c) 4

d) 1

Ans: c

Q 19) If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are

a) 2, 4, 6

b) 1, 5, 3

c) 2, 8, 4

d) 2, 3, 4

Ans: d

Explanation: Reason: Let three numbers be a – d, a, a + d

∴ a – d + a + a + d = 9

⇒ 3a = 9 ⇒ a = 3

Also (a – d) . a . (a + d) = 24

⇒ (3 -d) .3(3 + d) = 24

⇒ 9 – d² = 8

⇒ d² = 9 – 8 = 1

∴ d = ± 1

Hence numbers are 2, 3, 4 or 4, 3, 2

Q 20) The 10th term from the end of the A.P. -5, -10, -15,…, -1000 is

a) – 955

b) – 945

c) – 950

d) – 965

Ans: a

Q 21) The sum of all two digit odd numbers is

a) 2575

b) 2475

c) 2524

d) 2425

Ans: b

Q 22) Find the sum of 12 terms of an A.P. whose nth term is given by an = 3n + 4

(a) 262

(b) 272

(c) 282

(d) 292

Ans: a

Q 23) The sum of first n odd natural numbers is

(a) 2n²

(b) 2n + 1

(c) 2n – 1

(d) n²

Ans: d

Q 24) The sum of first n terms of the series a, 3a, 5a, …….. is

(a) na

(b) (2n – 1) a

(c) n²a

(d) n²a²

Ans: c

Q 25) If 2x, x + 10, 3x + 2 are in A.P., then x is equal to

(a) 0

(b) 2

(c) 4

(d) 6

Ans: d

Q 26) Which term of the AP: 27, 24, 21, ……… is zero?

(a) 8th

(b) 10th

(c) 9th

(d) 11th

Ans: b

Q 27) If 7 times the 7th term of an A.P. is equal to 11 times its 11th term, then 18th term is

(a) 18

(b) 9

(c) 77

(d) 0

Ans: d

Q 28) If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?

(a) 30

(b) 33

(c) 37

(d) 38

Ans: b

Q 29) Next term of the AP √2, 3√2, 5√2, ……. is

(a) 2√7

(6) 6√2

(c) 9√2

(d) 7√2

Ans: d

Q 30) If p, q, r and s are in A.P. then r – q is

(a) s – p

(b) s – q

(c) s – r

(d) none of these

Ans: c

Q 31) If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are

(a) 2, 4, 6

(b) 1, 5, 3

(c) 2, 8, 4

(d) 2, 3, 4

Ans: d

Q 32) If the sum of the first m terms of an AP is n and the sum of its n terms is m, then the sum of its (m + n) terms will be

(a) m + n

(b) -(m + n)

(c) m – n

(d) 0

Ans: b

Q 33) The (n – 1)th term of an A.P. is given by 7,12,17, 22,… is

(a) 5n + 2

(b) 5n + 3

(c) 5n – 5

(d) 5n – 3

Ans: d

Q 34) If a, b, c, d, e are in A.P., then the value of a – 4b + 6c – 4d + e is

(a) 0

(b) 1

(c) -1.

(d) 2

Ans: a

Explanation : Let common difference of A.P. be d

∴ b = a + d, c = a + 2d, d = a + 3d and e = a + 4d

Given equation a-4b + 6c-4d + c

= a – 4(a + d) + 6(a + 2d) – 4(a + 3d) + (a + 4d)

= a – 4a – 4d + 6a + 12d – 4a – 12d + a + 4d = 8a – 8a + 16d – 16d = 0

Q 35) nth term of the sequence a, a + d, a + 2d,… is

(a) a + nd

(b) a – (n – 1)d

(c) a + (n – 1)d

(d) n + nd

Ans: a

Q 36) If 2x, x + 10, 3x + 2 are in A.P., then x is equal to

(a) 0

(b) 2

(c) 4

(d) 6

Ans: d

Q 37) The 10th term from the end of the A.P. 4, 9,14, …, 254 is

(a) 209

(b) 205

(c) 214

(d) 213

Ans: a

Q 38) If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be

(a) A + B

(b) A – B

(c) 2A

(d) 2B

Ans: d

Q 39) The sum of all odd integers between 2 and 100 divisible by 3 is

(a) 17

(b) 867

(c) 876

(d) 786

Ans: b

Q 40) The sum of the first 15 multiples of 8 is

(a) 920

(b) 860

(c) 900

(d) 960

Ans: d

Q 41) The 21st term of the AP whose first two terms are –3 and 4 is

(a) 17

(b) 137

(c) 143

(d) –143

Ans: b

Q 42) If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?

(a) 30

(b) 33

(c) 37

(d) 38

Ans: b

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