Number Series— Concepts, Formulas & Shortcuts
- Step 1: take consecutive differences. Constant → arithmetic; growing regularly → check second differences.
- Step 2: take ratios. Constant ratio → geometric progression.
- Step 3: compare against squares (1, 4, 9, 16…), cubes (1, 8, 27, 64…) and primes (2, 3, 5, 7, 11…).
- Step 4: check the ×a + b pattern — e.g. 3, 7, 15, 31 is each term doubled plus one.
- Step 5: look for alternating series where odd and even positions follow separate rules.
- For "wrong number" questions, find the rule from the majority of terms and flag the outlier.
Number Series Practice Questions with Answers
Attempt each question first, then open the explanation. All 18 questions below are free to read and require no signup.
Q1.Find the next term: 2, 6, 12, 20, 30, ?
Easy- A38
- B40
- C42
- D44
Number Series question 1 of 18+Show Answer & Explanation
Answer: C. 42
Explanation: Differences are 4, 6, 8, 10, so the next difference is 12 → 30 + 12 = 42. (Also n(n+1): 1×2, 2×3, 3×4, …)
Q2.Find the next term: 3, 7, 15, 31, 63, ?
Moderate- A95
- B117
- C127
- D129
Number Series question 2 of 18+Show Answer & Explanation
Answer: C. 127
Explanation: Each term is the previous × 2 + 1: 63 × 2 + 1 = 127.
Q3.Find the next term: 1, 4, 9, 16, 25, ?
Easy- A30
- B32
- C36
- D49
Number Series question 3 of 18+Show Answer & Explanation
Answer: C. 36
Explanation: These are perfect squares 1², 2², 3², 4², 5², so next is 6² = 36.
Q4.Find the next term: 5, 11, 23, 47, ?
Moderate- A79
- B85
- C94
- D95
Number Series question 4 of 18+Show Answer & Explanation
Answer: D. 95
Explanation: Each term is doubled and increased by 1: 47 × 2 + 1 = 95.
Q5.Find the next term: 8, 27, 64, 125, ?
Easy- A180
- B196
- C216
- D256
Number Series question 5 of 18+Show Answer & Explanation
Answer: C. 216
Explanation: Cubes of 2, 3, 4, 5 → next is 6³ = 216.
Q6.Find the next term: 120, 99, 80, 63, 48, ?
Difficult- A35
- B36
- C38
- D40
Number Series question 6 of 18+Show Answer & Explanation
Answer: A. 35
Explanation: The terms are n² − 1 for n = 11, 10, 9, 8, 7 → next is 6² − 1 = 35.
Q7.Find the next term: 2, 3, 5, 7, 11, ?
Easy- A12
- B13
- C14
- D15
Number Series question 7 of 18+Show Answer & Explanation
Answer: B. 13
Explanation: The series lists consecutive prime numbers, so the next is 13.
Q8.Find the wrong number: 4, 8, 16, 32, 68, 128
Moderate- A16
- B32
- C68
- D128
Number Series question 8 of 18+Show Answer & Explanation
Answer: C. 68
Explanation: Each term should double: 32 × 2 = 64, not 68.
Q9.Find the next term: 6, 12, 24, 48, ?
Easy- A72
- B84
- C96
- D108
Number Series question 9 of 18+Show Answer & Explanation
Answer: C. 96
Explanation: Each term doubles: 48 × 2 = 96.
Q10.Find the next term: 1, 3, 6, 10, 15, ?
Moderate- A18
- B20
- C21
- D24
Number Series question 10 of 18+Show Answer & Explanation
Answer: C. 21
Explanation: These are triangular numbers with differences 2, 3, 4, 5 → next difference 6 gives 21.
Q11.Find the next term: 100, 90, 81, 73, ?
Moderate- A64
- B66
- C68
- D70
Number Series question 11 of 18+Show Answer & Explanation
Answer: B. 66
Explanation: Differences are −10, −9, −8, so the next is −7 → 73 − 7 = 66.
Q12.Find the missing term: 7, 21, 63, ?, 567
Moderate- A126
- B168
- C189
- D252
Number Series question 12 of 18+Show Answer & Explanation
Answer: C. 189
Explanation: Each term is multiplied by 3: 63 × 3 = 189.
Q13.Find the next term: 0, 1, 1, 2, 3, 5, ?
Easy- A6
- B7
- C8
- D9
Number Series question 13 of 18+Show Answer & Explanation
Answer: C. 8
Explanation: Fibonacci: each term is the sum of the previous two, so 3 + 5 = 8.
Q14.Find the wrong number: 5, 10, 20, 40, 75, 160
Moderate- A10
- B20
- C75
- D160
Number Series question 14 of 18+Show Answer & Explanation
Answer: C. 75
Explanation: The sequence should double each time: 40 × 2 = 80, not 75.
Q15.Find the next term: 2, 8, 18, 32, ?
Difficult- A40
- B48
- C50
- D54
Number Series question 15 of 18+Show Answer & Explanation
Answer: C. 50
Explanation: The terms are 2n²: 2, 8, 18, 32, so the next is 2 × 25 = 50.
Q16.Find the next term: 121, 144, 169, 196, ?
Moderate- A216
- B225
- C234
- D256
Number Series question 16 of 18+Show Answer & Explanation
Answer: B. 225
Explanation: These are squares of 11, 12, 13, 14 → next is 15² = 225.
Q17.Find the next term: 3, 6, 5, 10, 9, 18, ?
Difficult- A15
- B16
- C17
- D20
Number Series question 17 of 18+Show Answer & Explanation
Answer: C. 17
Explanation: The rule alternates ×2 then −1: 18 − 1 = 17.
Q18.Find the next term: 1, 4, 27, 256, ?
Difficult- A625
- B1,024
- C3,125
- D4,096
Number Series question 18 of 18+Show Answer & Explanation
Answer: C. 3,125
Explanation: The pattern is nⁿ: 1¹, 2², 3³, 4⁴, so the next is 5⁵ = 3,125.
Number Series — Frequently Asked Questions
What should I check first in a number series?+
Consecutive differences. If they are constant it is arithmetic; if they themselves form a pattern (4, 6, 8, 10) the series is quadratic. Only after differences fail should you test ratios and powers.
How do I spot an alternating series?+
If the differences swing wildly between large and small, split the series into odd-position and even-position terms and analyse the two sub-series separately.
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