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Number Series · Class 10

Number Series Questions for Class 10: Practice and Explanations

By the BrainSprint Editorial Team · Published

A number series is a list of numbers that follows a rule. Your job is to find the rule and use it to name the next term. Most Class 10 series questions use one of a small number of patterns, so a clear method helps you solve them quickly.

A four-step method

  1. Look at the differences. Subtract each term from the next. If the differences form a pattern, you have your rule.
  2. Look at the ratios. If the differences do not help, divide each term by the one before. A constant ratio means multiplication.
  3. Check for special numbers. Squares, cubes, primes and factorials appear often.
  4. Try alternating patterns. Sometimes two rules take turns, such as “multiply by 2, then subtract 1”.

Worked examples

Example A: 5, 8, 14, 23, 35, ? The differences are 3, 6, 9, 12. Each difference goes up by 3, so the next difference is 15. The next term is 35 + 15 = 50.

Example B: 3, 6, 5, 10, 9, 18, ? Look at the pairs. 3 becomes 6 by multiplying by 2, and 6 becomes 5 by subtracting 1. Then 5 becomes 10 (times 2), and 10 becomes 9 (minus 1). The pattern continues: 9 × 2 = 18, and 18 − 1 = 17.

Example C: 4, 9, 19, 39, 79, ? Each term is twice the previous term plus 1. So 2 × 79 + 1 = 159.

Practice questions

  1. 7, 11, 19, 35, ?
  2. 1, 2, 4, 7, 11, ?
  3. 2, 3, 5, 9, 17, ?
  4. 100, 96, 88, 72, ?
  5. 6, 12, 24, 48, ?

Answers and explanations

1. 67. Differences: 4, 8, 16. They double each time, so the next difference is 32. 35 + 32 = 67.

2. 16. Differences: 1, 2, 3, 4. The next difference is 5, so 11 + 5 = 16.

3. 33. Differences: 1, 2, 4, 8. The next difference is 16, so 17 + 16 = 33.

4. 40. Differences: −4, −8, −16. The next difference is −32, so 72 − 32 = 40.

5. 96. Each term is double the previous one. 48 × 2 = 96.

Common mistakes

  • Stopping after the first difference pattern. Always check whether the rule works for every term.
  • Assuming the rule is simple addition when the differences are growing.
  • Forgetting that the answer must follow the same rule, not just look sensible.

Practise in a challenge

Number series are a core part of the BrainSprint challenge. Play a Class 10 challenge to test these methods on ten fresh questions. For more practice, read our logical reasoning guide.

Planning your path after Class 10 or 12? Explore CareerSteps for career guidance.