Question 1

Find the next number in the series: 2, 6, 12, 20, 30, ?

Accepted Answer

Step 1: Identify the pattern by finding differences. First differences: 6-2=4, 12-6=6, 20-12=8, 30-20=10. Step 2: The first differences form an arithmetic sequence (4, 6, 8, 10). Step 3: Next first difference = 12. Step 4: Next number = 30 + 12 = 42.

Question 2

What is the missing number in the series: 5, 10, 20, 40, ?, 160?

Accepted Answer

Step 1: Identify the pattern by examining ratios. 10÷5=2, 20÷10=2, 40÷20=2. Step 2: Each term is double the previous term (geometric sequence with ratio 2). Step 3: Missing term = 40 × 2 = 80. Step 4: Verify: 80 × 2 = 160 ✓

Question 3

Find the next term in the series: 1, 1, 2, 3, 5, 8, 13, ?

Accepted Answer

Step 1: Recognize this as the Fibonacci sequence where each term is the sum of the two preceding terms. Step 2: Verify: 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13. Step 3: Next term = 8 + 13 = 21.

Question 4

What is the next term in the series: 3, 9, 27, 81, ?

Accepted Answer

Step 1: Identify the pattern by examining ratios. 9÷3=3, 27÷9=3, 81÷27=3. Step 2: This is a geometric sequence with common ratio 3. Step 3: Each term is 3 raised to successive powers: 3¹, 3², 3³, 3⁴. Step 4: Next term = 81 × 3 = 243 (or 3⁵).

Question 5

Find the missing number in the series: 2, 8, 18, 32, 50, ?

Accepted Answer

Step 1: Examine the relationship to perfect squares. 2=1×2, 8=2×4, 18=3×6, 32=4×8, 50=5×10. Step 2: Pattern is n(2n) where n=1,2,3,4,5,... Step 3: For n=6: 6×12 = 72.

Question 6

What is the next number in the series: 100, 99, 97, 94, 90, ?

Accepted Answer

Step 1: Find first differences: 99-100=-1, 97-99=-2, 94-97=-3, 90-94=-4. Step 2: The differences form the sequence -1, -2, -3, -4. Step 3: Next difference = -5. Step 4: Next number = 90 + (-5) = 85.

Question 7

In a number series, the first term is 5 and each subsequent term is obtained by multiplying the previous term by 2 and then subtracting 3. What is the 5th term of this series?

Accepted Answer

Step 1: Term 1 = 5. Step 2: Term 2 = 5 × 2 − 3 = 10 − 3 = 7. Step 3: Term 3 = 7 × 2 − 3 = 14 − 3 = 11. Step 4: Term 4 = 11 × 2 − 3 = 22 − 3 = 19. Step 5: Term 5 = 19 × 2 − 3 = 38 − 3 = 35. Therefore, the 5th term is 35.

Question 8

A series has the property that each term is the sum of the two preceding terms. If the 3rd term is 5 and the 4th term is 8, what is the 1st term?

Accepted Answer

Step 1: Let the 1st term = a and 2nd term = b. Step 2: By the given property, 3rd term = a + b = 5. Step 3: 4th term = b + (a + b) = a + 2b = 8. Step 4: From equation 1: a = 5 − b. Step 5: Substitute into equation 2: (5 − b) + 2b = 8, so 5 + b = 8, thus b = 3. Step 6: Therefore, a = 5 − 3 = 2. The 1st term is 2.

Question 9

In a number series, the sum of the first n terms is given by Sₙ = n² + 2n. What is the 4th term of the series?

Accepted Answer

Step 1: The nth term aₙ = Sₙ − Sₙ₋₁ for n ≥ 2. Step 2: S₄ = 4² + 2(4) = 16 + 8 = 24. Step 3: S₃ = 3² + 2(3) = 9 + 6 = 15. Step 4: a₄ = S₄ − S₃ = 24 − 15 = 9. Therefore, the 4th term is 9.

Question 10

A series is defined as: a₁ = 10, and aₙ = aₙ₋₁ + 2n for n ≥ 2. Find a₅.

Accepted Answer

Step 1: a₁ = 10. Step 2: a₂ = a₁ + 2(2) = 10 + 4 = 14. Step 3: a₃ = a₂ + 2(3) = 14 + 6 = 20. Step 4: a₄ = a₃ + 2(4) = 20 + 8 = 28. Step 5: a₅ = a₄ + 2(5) = 28 + 10 = 38. Therefore, a₅ = 38.

Question 11

In a series, the difference between consecutive terms increases by 1 each time. If the first term is 2 and the second term is 3, what is the 6th term?

Accepted Answer

Step 1: First term = 2, Second term = 3. Difference = 3 − 2 = 1. Step 2: The difference increases by 1 each time, so next differences are 2, 3, 4, 5. Step 3: Term 3 = 3 + 2 = 5. Step 4: Term 4 = 5 + 3 = 8. Step 5: Term 5 = 8 + 4 = 12. Step 6: Term 6 = 12 + 5 = 17. Therefore, the 6th term is 17.

Question 12

A number series follows the pattern: 3, 6, 12, 24, 48, ... What is the 8th term?

Accepted Answer

Step 1: Identify the pattern—each term is double the previous term (geometric series with ratio r = 2). Step 2: Term 1 = 3, Term 2 = 6, Term 3 = 12, Term 4 = 24, Term 5 = 48. Step 3: Term 6 = 48 × 2 = 96. Step 4: Term 7 = 96 × 2 = 192. Step 5: Term 8 = 192 × 2 = 384. Therefore, the 8th term is 384.

Question 13

A series has terms where aₙ = (n³ - n)/3 for positive integers n. Which of the following is NOT a term in this series?

Accepted Answer

Step 1: Check the formula aₙ = (n³ - n)/3 = n(n² - 1)/3 = n(n-1)(n+1)/3. Step 2: This is the product of three consecutive integers divided by 3, which is always an integer. Step 3: Compute terms: a₁ = (1-1)/3 = 0, a₂ = (8-2)/3 = 2, a₃ = (27-3)/3 = 8, a₄ = (64-4)/3 = 20, a₅ = (125-5)/3 = 40, a₆ = (216-6)/3 = 70. Step 4: The series is 0, 2, 8, 20, 40, 70, ... Step 5: Check which option is missing: 30 is not in this sequence (it lies between 20 and 40 but is not produced by any integer n).

Question 14

In a number series, the first term is 2 and each subsequent term is obtained by multiplying the previous term by 3 and then subtracting 1. What is the 5th term of this series?

Accepted Answer

Step 1: Term 1 = 2. Step 2: Term 2 = 2×3 - 1 = 5. Step 3: Term 3 = 5×3 - 1 = 14. Step 4: Term 4 = 14×3 - 1 = 41. Step 5: Term 5 = 41×3 - 1 = 122. Therefore, the 5th term is 122.

Question 15

A series is defined as: a₁ = 3, and aₙ = aₙ₋₁² - 2aₙ₋₁ for n ≥ 2. Find a₄.

Accepted Answer

Step 1: a₁ = 3. Step 2: a₂ = 3² - 2(3) = 9 - 6 = 3. Step 3: a₃ = 3² - 2(3) = 9 - 6 = 3. Step 4: a₄ = 3² - 2(3) = 9 - 6 = 3. The series becomes constant at 3. Therefore, a₄ = 3.

Question 16

In a series, aₙ = aₙ₋₁ + aₙ₋₂ (Fibonacci-like), with a₁ = 2 and a₂ = 3. What is the sum of the first 7 terms?

Accepted Answer

Step 1: a₁ = 2, a₂ = 3. Step 2: a₃ = 2 + 3 = 5. Step 3: a₄ = 3 + 5 = 8. Step 4: a₅ = 5 + 8 = 13. Step 5: a₆ = 8 + 13 = 21. Step 6: a₇ = 13 + 21 = 34. Step 7: Sum = 2 + 3 + 5 + 8 + 13 + 21 + 34 = 86. Therefore, the sum of the first 7 terms is 86.

Question 17

In a series, the difference between consecutive terms follows a pattern: 1st difference is 2, 2nd difference is 5, 3rd difference is 10, 4th difference is 17. If the first term is 5, what is the 5th term?

Accepted Answer

Step 1: First term = 5. Step 2: 2nd term = 5 + 2 = 7. Step 3: 3rd term = 7 + 5 = 12. Step 4: 4th term = 12 + 10 = 22. Step 5: 5th term = 22 + 17 = 39. Step 6: Verify the difference pattern: differences are 2, 5, 10, 17 (which are n² + 1 for n = 1,2,3,4). Therefore, the 5th term is 39.

SSC CPO Number Series

SSC CPO Number Series — Past Exam Questions

Number Series— Rules & Concept

Key Points to Remember

Exam-Specific Tips

60-Second Revision — Number Series