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Gyaan Maths
CBSE · Class 6-10
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CBSE Maths · Class 10

Chapter 5: Arithmetic Progressions

Name: ________________________
Date: ______________
Marks: ____ / 10

Sequences where each term differs from the previous by a fixed common difference; formulas for the nn-th term and sum of the first nn terms.

Questions

  1. S20S_{20} of 5,8,11,…5, 8, 11, \ldots
  2. Which term of 21,18,15,…21, 18, 15, \ldots is −81-81?
  3. Find a25a_{25} of 2,5,8,…2, 5, 8, \ldots
  4. Sum of first 5050 natural numbers.
  5. ana_n of AP 10,7,4,…10, 7, 4, \ldots when n=15n = 15.
  6. How many terms of 2,4,6,…2, 4, 6, \ldots add to 110110?
  7. Three numbers in AP have sum 2424 and product 440440.
  8. Which term of the AP 3,8,13,…3, 8, 13, \ldots is 7878?
  9. Sum of first nn terms is 3n2+5n3n^2 + 5n. Find nthn^{th} term.
  10. The 7th term of an AP is 34 and 13th is 64. Find the AP.

Extra Practice (Optional)

  • Sum of first 100100 multiples of 33.
  • If a3=5,a7=9a_3 = 5, a_7 = 9, find AP.
  • Middle term of an AP with 99 terms.
  • Sum of first 5050 even numbers.
  • S20−S10S_{20} - S_{10} for an AP with a=2,d=3a=2, d=3.

Answer Key (For Teachers)

  1. Answer: 670670.
    Working: a=5,d=3a = 5, d = 3; S20=10(10+57)S_{20} = 10(10 + 57).
  2. Answer: 35th35^{th}.
    Working: Set 21+(n−1)(−3)=−8121 + (n-1)(-3) = -81.
  3. Answer: 7474.
    Working: 2+24⋅32 + 24\cdot 3.
  4. Answer: 12751275.
    Working: n(n+1)/2n(n+1)/2.
  5. Answer: −32-32.
    Working: a=10,d=−3a = 10, d = -3; a15=10+14(−3)a_{15} = 10 + 14(-3).
  6. Answer: 1010.
    Working: Sn=n(n+1)=110S_n = n(n+1) = 110.
  7. Answer: 5,8,115, 8, 11.
    Working: Take a−d,a,a+da-d, a, a+d; 3a=24,a=83a = 24, a = 8; then d2=9d^2 = 9.
  8. Answer: 16th16^{th}.
    Working: 3+(n−1)5=78⇒n=163 + (n-1)5 = 78 \Rightarrow n = 16.
  9. Answer: 6n+26n + 2.
    Working: an=Sn−Sn−1a_n = S_n - S_{n-1}. → =(3n2+5n)−(3(n−1)2+5(n−1))=6n+2= (3n^2 + 5n) - (3(n-1)^2 + 5(n-1)) = 6n + 2.
  10. Answer: 4,9,14,…4, 9, 14, \ldots
    Working: a+6d=34,  a+12d=64a + 6d = 34,\; a + 12d = 64. → Subtract: 6d=30⇒d=5,a=46d = 30\Rightarrow d = 5, a = 4.
Gyaan Maths · CBSE Class 10 · Chapter 5
Gyaan Maths — CBSE Class 6-10, built for board-toppers.
v1.1 · Feb 2026