Please refer to the MCQ Questions for Class 10 Arithmetic Progression Maths Chapter 6 with Answers. The following Arithmetic Progression Class 10 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 10. Our experts have designed MCQ Questions for Class 10 Arithmetic Progression with Answers for all chapters in your NCERT Class 11 Mathematics book. You can access all MCQs for Class 10 Mathematics

## Arithmetic Progression Class 10 MCQ Questions with Answers

See below Arithmetic Progression Class 10 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question. If 9 ^{th} term of an A.P. is zero, then its 29^{th} term is ________ its 19^{th }term.**

(A) Thrice of

(B) Twice of

(C) Half of

(D) Equal to

## **Answer**

A

**Question.** Find the sum of first 20 terms of an A.P. whose n^{th} term is given by T_{n} = (7 – 3n).

(A) 382

(B) –490

(C) 420

(D) –382

## **Answer**

B

**Question.** In an A.P., the sum of first n terms is 3n^{2}/2 + 13n/2 Find its 25^{th} term.

(A) 80

(B) 120

(C) 60

(D) 78

## **Answer**

A

**Question.** Which term of the A.P. 5, 2, –1, ……. is –22 ?

(A) 9

(B) 11

(C) 10

(D) 7

## **Answer**

C

**Question.** The sum of all terms of the arithmetic progression having ten terms except for the first term, is 99, and except for the sixth term, is 89. Find the 8^{th} term of the progression if the sum of the first and the fifth term is equal to 10.

(A) 15

(B) 25

(C) 18

(D) 10

## **Answer**

A

**Question.** In an A.P., if the p^{th} term is ‘q’ and the q^{th} term is ‘p’, then its n^{th} term is ________.

(A) p + q – n

(B) p + q + n

(C) p – q + n

(D) p – q – n

## **Answer**

A

**Question**. If x ≠ y and the sequences x, a_{1}, a_{2}, y and x, b_{1}, b_{2}, y each are in A.P., then (a_{2} – a_{1} / b_{2} – b_{1}) is ________.

(A) 2/3

(B) 3/2

(C) 1

(D) 3/4

## **Answer**

C

**Question.** The ratio of the sum of m and n terms of an A.P. is m^{2} : n^{2}, then find the ratio of m^{th} and nth terms.

(A) 2m + 1 : 2n + 1

(B) 2m – 1 : 2n – 1

(C) 2m : n

(D) m : n

## **Answer**

B

**Question.** Four numbers are inserted between the numbers 4 and 39 such that an A.P. results. Find the biggest of these four numbers.

(A) 33

(B) 31

(C) 32

(D) 30

## **Answer**

C

**Question.****If the m ^{th} term of an A.P. is 1/n and nth term is 1/m , then the sum of first m^{n }terms is _______.**

(A) mn + 1

(B) mn +1/2

(C) mn −1/2

(D)mn −1/3

## **Answer**

B

**Question.** The production of TV in a factory increases uniformly by a fixed number every year. It produced 8000 sets in 6^{th} year and 11300 in 9^{th} year. Find the production in the 6 years.

(A) 40500

(B) 20000

(C) 20500

(D) 31500

## **Answer**

D

**Question.** Deepak repays his total loan of ₹1,18,000 by paying every month starting with the first instalment of ₹1000. If he increases the instalment by ₹100 every month. what amount will be paid as the last instalment of loan?

(A) ₹ 4900

(B) ₹ 5400

(C) ₹ 3500

(D) ₹ 4500

## **Answer**

A

**Question.** A manufacturer of laptop produced 6000 units in 3^{rd} year and 7000 units in the 7^{th} year. Assuming that production increases uniformly by a fixed number every year, find the production in the 5^{th} year.

(A) 6500 units

(B) 5000 units

(C) 6000 units

(D) 8000 units

## **Answer**

A

**Question.** Raghav buys a shop for ₹ 120000. He pays half of the amount in cash and agrees to pay the balance in 12 annual instalments of ₹ 5000 each. If the rate of interest is 12% and he pays the interest due on the unpaid amount with the instalment. Find the total cost of the shop.

(A) ₹ 156800

(B) ₹ 156700

(C) ₹ 165200

(D) ₹ 166800

## **Answer**

D

**Question.** There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardner will cover in order to water all the trees.

(A) 3000 m

(B) 3500 m

(C) 3800 m

(D) 4000 m

## **Answer**

B

**Question.** Which of the following statements is INCORRECT?

(a) Sum of n terms of the list of numbers √2 √8 √18 √32……is n(n + 1)/√2

(b) The common difference of the A.P. given by a_{n} = 3n + 2 is 3.

(c) The sum of the A.P. (–5), (–8), (–11), …, (–230) is – 8930.

(A) Only (a)

(B) Only (b)

(C) Both (a) and (b)

(D) (a), (b) and (c)

## **Answer**

D

** Question. If there are (2n + 1) terms in A.P., then find the ratio of the sum of odd terms and the sum of even terms.**(A) n : (n + 1)

(B) (n + 1) : n

(C) n : (n + 2)

(D) (n + 2) : n

## **Answer**

B

**Question.** if a^{n+1} + b^{n+1}/a^{n}+b^{n} is the A.M. between a and b, then find the value of n.

(A) 0

(B) 1

(C) 2

(D) 3

## **Answer**

A

**Question.** The sum of the third and seventh terms of an A.P. is 6 and their product is 8. Find the sum of first sixteen terms of the A.P.

(A) 86

(B) 90

(C) Both (A) and (B)

(D) None of these

## **Answer**

D

**Question.****Fill in the blanks.**

(i) If the ratio of sum of n terms of two A.P. is (7n + 1) : (4n + 27), then ratio of their m^{th} terms is **P** .

(ii) Sum of n odd natural numbers is **Q**** **.

(iii) If sum of n terms of three A.P. are S_{1}, S_{2}, S_{3}. The first term of each is 1 and common difference are 1, 2 and 3 respectively, then S_{1} + S_{3} / S_{2} = R

## **Answer**

A

**Question.****Which is the first negative term of the arithmetic progression 35, 30, 25,…..?**

(a) 7^{th} term

(b) 5^{th} term

(c) 9^{th} term

(d) 11^{th} term

## **Answer**

C

**Question.****The sum to ‘n’ natural numbers is S _{1 }sum of the squares of ‘n’ natural numbers is S_{2} and sum of the cubes of ‘n’ natural numbers is S_{3 }Which of the following is equal to 9S^{2}_{2} ?**

(a) (1 – 8S1 )S

_{2}

(b) S

_{3}(1 + 8S

_{1})

(c) S

_{1}(1 + 8S

_{2})

(d) S

_{1}(1 – 8S

_{3})

## **Answer**

B

**Question.** What is the term of an arithmetic progression whose sum to ‘n’ terms is 2n^{2}-3n ?

(a) 4n – 3

(b) 4n – 5

(c) 4n + 5

(d) 5 – 4n

## **Answer**

B

**Question.** In an arithmetic progression, if t_{p} = q, t_{q} = p, find t_{pq} .

(a) p + q – p_{q}

(b) p + q

(c) p – q + p_{q}

(d) p_{q} – p – q

## **Answer**

A

**Question.** There are ‘n’ arithmetic means in between ‘a’ and ‘b’. Find the common difference.

(a) b – a / n + 1

(b) b + a / n – 1

(c) b – a / n – 1

(d) b + a / n + 1

## **Answer**

A

**Question.** The numbers 28, 22, ‘x’, ‘y’, 4 are in arithmetic progression. What are the respective values of ‘x’ and ‘y’?

(a) 10, 16

(b) 20, 18

(c) 18, 16

(d) 16, 10

## **Answer**

D

**Question.** In an arithmetic progression, the fourth term is 8 and the sum of 12 terms is 156. Find the value of ‘p’ if the th p term is 1000.

(a) 200

(b) 500

(c) 300

(d) 100

## **Answer**

B

**Question.** What is the sum of first ‘n’ odd numbers starting from 11?

(a) n^{2} + 10n

(b) n^{2} – 10n

(c) 10n – n^{2}

(d) n^{2}

## **Answer**

A

**Question.** Divide 21 into three parts that are in arithmetic progression and whose product is 168.

(a) 3, 6, 9

(b) 14, 17, 11

(c) 2, 6, 14

(d) 2, 7, 12

## **Answer**

D

**Question.** Find the number of terms of the arithmetic progression 1/3, 1/2. 2/3,……….. 11/6

(a) 8

(b) 10

(c) 12

(d) 13

## **Answer**

B

**Question.** An arithmetic progression has a 3rd term of 13 and a last term of 148. If the common difference is 5, find the number of terms of the progression.

(a) 30

(b) 40

(c) 50

(d) 75

## **Answer**

A

**Question.** Which of the following is incorrect?

(a) S_{n} of the arithmetic progression 3,13,23,…. is 5n^{2} – 8n .

(b) s_{n} = 3n^{2} – 8n is the sum of an arithmetic progression whose common difference is 6.

(c) n^{th} term, t_{n} = s_{n} – s_{n-1}

(d) The nth term of an arithmetic progression is t_{n }= a + (n -1) d .

## **Answer**

A

**Question.** Identify the formula for then n^{th} term of the arithmetic progression whose first term,

(a) is 2 – x, and the common difference,

(d) is ‘x’.

(a) 2 + x – nx

(b) 2 + (n – 2)x

(c) 2 – x – nx

(d) 2 + (n – 1)x

## **Answer**

B

**Question.** In an arithmetic progression if 7 times the 7^{th} term is equal to 11 times the 11^{th} term, find its 18^{th} term.

(a) 1

(b) 0

(c) -1

(d) 2

## **Answer**

B

**Question.** Find the sum of the numbers in between 1 and 1000 which are divisible by 9.

(a) 55944

(b) 54954

(c) 99994

(d) 99894

## **Answer**

A

**Question.****What is the sum to ‘n’ terms of the series √5,√20,√45,√80,…..?**

(a) n(n+1)√5/2

(b) n(n+1)/√2

(c) n/2((n+1)√5)

(d) n(n +1)√5

## **Answer**

A

**Question.** Find the sum of

**terms.**

(a) n/2

(b) n – 1 / 2

(c) n + 1 / 2

(d) n(n + 1) / n^{2}

## **Answer**

B

**Question.****How many terms of the arithmetic progression 1, 9, 17, …. must be taken to give a sum of 1540?**

(a) 10

(b) 40

(c) 20

(d) 15

## **Answer**

C

** Question.** In an AP, if a = 3.5, d = 0, n = 101, then an will be

(A) 0

(B) 3.5

(C) 103.5

(D) 104.5

## **Answer**

(B)**Explanation:**

For an A.P

an = a + (n – 1) d

= 3.5 + (101 – 1)x0

= 3.5

** Question.** In an AP, if d = –4, n = 7, an = 4, then a is

(A) 6

(B) 7

(C) 20

(D) 28

## **Answer**

(D)**Explanation:**

For an A.P

a^{n} = a + (n – 1) d

4 = a + (7 – 1) (-4)

4 = a + 6 (-4)

4 + 24 = a

a = 28

**Question.****The first four terms of an AP, whose first term is –2 and the common difference is –2, are**

(A) – 2, 0, 2, 4

(B) – 2, 4, – 8, 16

(C) – 2, – 4, – 6, – 8

(D) – 2, – 4, – 8, –16

## **Answer**

(C)**Explanation:**

Let the first four terms of a_{n} A.P are a, a+d, a+2d and a+3d

Given that the first termis −2 and difference is also −2, then the A.P would be:

-2,(-2-2), [-2+2(-2)],[-2 + 3(-2)]

= – 2, – 4, – 6, – 8

**Question.****The 11th term of an A.P – 5 -(5/2),0,(5/2) …………….is:**

(A) –20

(B) 20

(C) –30

(D) 30

## **Answer**

(B)**Explanation:**

Given A.P is – 5 -(5/2),0,(5/2)

here a = – 5

d = -5/2 – (-5)

d = 5/2

a_{11} = a + (11 -1)d

a_{11} = – 5 + 10 (5/2)

a_{11} = – 5 + 25

a_{11} = 20

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

(A) Pythagoras

(B) Newton

(C) Gauss

(D) Euclid

## **Answer**

(C)**Explanation:**

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

**One Word Questions :**

**Question. If first term of an A.P. is 3 and 11th term is 43, find the common difference.**

**Answer**

4

**Question. If 7th term of an A.P. is zero then what is the relation between 17th and 37th term?**

**Answer**

Thrice

**Question. If the 9th term of an A.P. is zero, then what is the ratio of 29th term to 19th term?**

**Answer**

2 : 1

**Question. If 4th and 8th terms of an A.P. are 11 and 23 respectively, find a and d.**

**Answer**

a = 2, d = 3

**Question. Find the value of d of the A.P. whose nth term is 9 –5n.**

**Answer**

–5

**Question. If three consecutive terms of an A.P. are a – d, a, a + d and their sum is 54 and d is 7, find the three terms.**

**Answer**

11, 18, 25

**Question. If a = 5, d = –1, then which term of the A.P. is zero?**

**Answer**

6

**Question. Find the value of 11th term of the A.P., whose first two terms are –3 and 4.**

**Answer**

67

**Question. What should be added to 184 to become the term of the sequence 3, 7, 11,…….?**

**Answer**

3

**Question. Find the common difference d of the A.P. 10, 8, 6, 4, 2 ……..**

**Answer**

–2

**Question. If 7th term of an A.P. is 32 and 13th term is 62. Find the series.**

**Answer**

2, 7, 12, ……

**Question. Find the number of terms of the A.P. 5, 9, 13, 17, 21, 25, 29, …… 41**

**Answer**

10

**Question. Find the number of terms of the A.P. 1, 4, 7, 10, …… 61.**

**Answer**

21

**Question. If Rajni goes from Rohini to Lajpat Nagar with a speed of 30km/hr by car and after every hour she increases the speed by 5km/hr., then what is the speed of car after 4 hours?**

**Answer**

50km/hr.

**Question. Find the sum of all terms of the A.P. 1 + 3 + 5 + ……. + 29.**

**Answer**

225

**Question. If 7th and 6th terms of an A.P. are 25 and 32, what is the value of d?**

**Answer**

– 7

**Question. Determine ‘k’ so that 8k + 4, 6k – 2, 2k – 7 are three consecutive terms of an A.P.**

**Answer**

1/2

**Question. Find the sum of first 5 terms of the A.P. 3, 7, 11…….**

**Answer**

55

**Question. What is the sum of first five multiples of 3?**

**Answer**

45

**Question. Find the sum 2 + 6 + 10 + 14 + ……. + 34.**

**Answer**

162

**Question. Find the 6th term of an A.P. 3, 5, 7……**

**Answer**

13

**Question. 1, 4, 7, 10, 13 …… is an A.P. Find ‘d’.**

**Answer**

3

**Question. If S _{n} and S_{n–1} are given, then what is S_{n} – S_{n–1}?**

**Answer**

t_{n}

**Question. Find the sum of first 10 natural numbers.**

**Answer**

55

**Question. If tn = 2n+1 then find the series.**

**Answer**

3, 5, 7,…..