LIWA

Arithmetic Progressions

CBSE Class 10 · Maths · Chapter 5

Past board exam questions

CBSE 2027 sample paper · 1 mark

The middle term of the A.P.: 10, 7, 4, …, – 62 is:

  1. – 26
  2. – 29
  3. – 32
  4. – 35
Show answer
– 26

CBSE 2027 sample paper · 1 mark

The first term of AP is p and the common difference is q, then its 10th term is

  1. q + 10p
  2. p - 9q
  3. p + 9q
  4. p + 10q
Show answer
p + 9q

CBSE 2027 sample paper · 3 marks

Ridhi drew a polygon with n sides. The smallest exterior angle is 8° and each subsequent exterior angle is 4° more than the previous exterior angle. Find the number of sides of the polygon that Ridhi had drawn.

Show answer
The exterior angles form an A.P. with a = 8 and d = 4. Sum of all exterior angles of a polygon = 360°, so Sn = 360. (n)/(2)[2 × 8 + (n - 1) × 4] = 360 ⇒ n(2n + 6) = 360 ⇒ n2 + 3n - 180 = 0 ⇒ (n + 15)(n - 12) = 0 ⇒ n = -15 or 12. n cannot be negative, so n = 12. The polygon has 12 sides.

CBSE 2027 sample paper · 4 marks

Delhi's pollution is a severe, often seasonal issue caused by a combination of factors like high vehicular and industrial emissions, dust from construction, and crop burning in surrounding states. In a school, students of classes I to XII thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees that each section of each class will plant be three more than the double of the class in which they are studying, e.g., a section of class IV will plant 11 trees. If in the given school, there are two sections of each class, then answer the following questions: (i) If number of trees planted by students class-wise follow arithmetic progression, then find the common difference. (1) (ii) What is the number of trees planted by students of class VI? (1) (iii)(A) What is the total number of trees planted by the students of given school? (2) OR (iii)(B) Identify the class that planted 34 trees. (2)

Show answer
Trees planted by class n (two sections) = 2(2n + 3): class I = 10, class II = 14, class III = 18, … — an AP 10, 14, 18, 22, … (i) Common difference = 14 - 10 = 4. (ii) Class VI: 2\2(6) + 3\ = 30 trees. (iii)(A) Total = S12 = (12)/(2)\2(10) + (12 - 1)4\ = 6 × 64 = 384 trees. OR (iii)(B) Let the class be n: 2(2n + 3) = 34 ⇒ 2n + 3 = 17 ⇒ n = 7. Class VII planted 34 trees.

CBSE 2027 sample paper · 3 marks

Find the sum of integers between 1 and 400 that are multiples of 4 as well as of 5.

Show answer
Multiples of both 4 and 5 are multiples of LCM (4, 5) = 20: 20, 40, 60, …, 380 (400 is not between 1 and 400). a = 20, d = 20, an = 380 ⇒ 20 + (n - 1)20 = 380 ⇒ n = 19. S19 = (19)/(2)[20 + 380] = 3800.

CBSE 2026 board paper · 1 mark

The number of multiples of 6 lying between 25 and 363 is :

  1. 56
  2. 56·5
  3. 57
  4. 58
Show answer
56

CBSE 2026 board paper · 1 mark

If an represents nth term of the A.P. -(15)/(4), -(10)/(4), -(5)/(4), ldots then value of a16 - a12 is

  1. 4
  2. (5)/(4)
  3. 5
  4. (25)/(4)
Show answer
5

CBSE 2026 board paper · 1 mark

The nth term of an A.P. is √(2) n + 1. Its common difference is

  1. √(2)
  2. √(2) n
  3. 1
  4. √(2) + 1
Show answer
√(2)