Number series

PYQ (2016-2025 papers)

• 2025 · G4 · Question 148 · Final answer key
• 2025 · G4 · Question 149 · Final answer key
• 2025 · G4 · Question 152 · Final answer key
• 2024 · G4 · Question 137 · Final answer key
• 2024 · G4 · Question 191 · Final answer key
• 2022 · G4 · Question 130 · Final answer key
• 2022 · G4 · Question 174 · Final answer key
• 2019 · G4 · Question 197 · Final answer key
• 2019 · G4 · Question 198 · Final answer key
• 2019 · G4 · Question 199 · Final answer key
• 2019 · G4 · Question 200 · Final answer key
• 2018 · G4 · Question 118 · Final answer key
• 2018 · G4 · Question 122 · Final answer key
• 2018 · G4 · Question 165 · Final answer key
• 2018 · G4 · Question 168 · Final answer key
• 2018 · G4 · Question 170 · Final answer key
• 2018 · G4 · Question 173 · Final answer key
• 2018 · G4 · Question 174 · Final answer key
• 2016 · G4 · Question 147 · Final answer key
• 2016 · VAO · Question 116 · Final answer key
• 2016 · VAO · Question 118 · Final answer key

Free questions

1. Question 1

   A sequence is defined by a₁ = 2, a₂ = 2 and aₙ = aₙ₋₁ / (aₙ₋₂ + 2) for n ≥ 3. What is its 5th term?

   1. A. 1/8
   2. B. 1/20
   3. C. 1/11
   4. D. 1/16
   Answer and explanation

   ✓ Correct answer: B. 1/20

   a₃ = a₂/(a₁ + 2) = 2/4 = 1/2; a₄ = a₃/(a₂ + 2) = (1/2)/4 = 1/8; a₅ = a₄/(a₃ + 2) = (1/8) ÷ (5/2) = 1/20.

   Source: கணிதம், பத்தாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard X, Tamil medium; Samacheer Kalvi) (இயல் 2 எண்களும் தொடர்வரிசைகளும் (2.6 தொடர்வரிசைகள்), p. 55 (PDF p. 61))

2. Question 2

   Consider the following statements on sequences. 1. A sequence with a finite number of terms is a finite sequence. 2. A sequence with an infinite number of terms is an infinite sequence. 3. Every function is a sequence. Which of these are correct?

   1. A. 1 only
   2. B. 2 and 3 only
   3. C. 1 and 3 only
   4. D. 1 and 2 only
   Answer and explanation

   ✓ Correct answer: D. 1 and 2 only

   Finitely many terms make a finite sequence and infinitely many an infinite one; every sequence is a function, but not every function is a sequence; so 1 and 2 are correct and 3 is wrong.

   Source: கணிதம், பத்தாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard X, Tamil medium; Samacheer Kalvi) (இயல் 2 எண்களும் தொடர்வரிசைகளும் (2.6 தொடர்வரிசைகள்), p. 53 (PDF p. 59))

3. Question 3

   What is the next term of the sequence 1/3, 1/7, 1/11, 1/15, ...?

   1. A. 1/16
   2. B. 1/60
   3. C. 5/19
   4. D. 1/19
   Answer and explanation

   ✓ Correct answer: D. 1/19

   The numerator stays 1; the denominators 3, 7, 11, 15 grow by 4; the next denominator is 15 + 4 = 19, so the next term is 1/19.

   Source: கணிதம், பத்தாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard X, Tamil medium; Samacheer Kalvi) (இயல் 2 எண்களும் தொடர்வரிசைகளும் (2.6 தொடர்வரிசைகள்), p. 54 (PDF p. 60))