Question 1

Find the missing number in the series: 1, 4, 9, 16, 25, ?, 49

Accepted Answer

Step 1: Recognize that each term is a perfect square. 1=1², 4=2², 9=3², 16=4², 25=5². Step 2: The pattern shows consecutive perfect squares. Step 3: The missing term should be 6²=36. Step 4: Verify: 7²=49 ✓

Question 2

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) with common difference 2. Step 3: Next first difference = 10+2=12. Step 4: Next term = 30+12=42.

Question 3

Find the next number: 2, 3, 5, 8, 13, 21, ?

Accepted Answer

Step 1: Check if each term is the sum of the previous two terms. 2+3=5 ✓, 3+5=8 ✓, 5+8=13 ✓, 8+13=21 ✓. Step 2: This is a Fibonacci-type sequence. Step 3: Next term = 13+21=34.

Question 4

What is the next term in the series: 5, 10, 20, 40, 80, ?

Accepted Answer

Step 1: Check the ratio between consecutive terms. 10÷5=2, 20÷10=2, 40÷20=2, 80÷40=2. Step 2: This is a geometric series with common ratio r=2. Step 3: Next term = 80×2=160.

Question 5

What comes next in the series: 3, 6, 11, 18, 27, ?

Accepted Answer

Step 1: Find first differences: 6-3=3, 11-6=5, 18-11=7, 27-18=9. Step 2: First differences are 3, 5, 7, 9 (odd numbers increasing by 2). Step 3: Next first difference = 9+2=11. Step 4: Next term = 27+11=38.

Question 6

What is the next term in the series: 100, 50, 25, 12.5, ?

Accepted Answer

Step 1: Check the ratio between consecutive terms. 50÷100=0.5, 25÷50=0.5, 12.5÷25=0.5. Step 2: This is a geometric series with common ratio r=0.5 (or dividing by 2). Step 3: Next term = 12.5÷2=6.25.

Question 7

In a series, the difference between consecutive terms increases by 1 each time. 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: Third term = 3 + 2 = 5 (difference increases by 1, so now 2). Step 3: Fourth term = 5 + 3 = 8 (difference is 3). Step 4: Fifth term = 8 + 4 = 12 (difference is 4). Step 5: Sixth term = 12 + 5 = 17 (difference is 5). Therefore, the 6th term is 17.

Question 8

A series has the pattern: 2, 5, 10, 17, 26, ?. What is the next term?

Accepted Answer

Step 1: Find the differences between consecutive terms: 5 − 2 = 3, 10 − 5 = 5, 17 − 10 = 7, 26 − 17 = 9. Step 2: The differences are 3, 5, 7, 9 (odd numbers increasing by 2). Step 3: The next difference should be 11. Step 4: Next term = 26 + 11 = 37. Therefore, the next term is 37.

Question 9

In a series, every term is the sum of the two preceding terms. If the first term is 2 and the second term is 3, what is the 7th term?

Accepted Answer

Step 1: Term 1 = 2, Term 2 = 3. Step 2: Term 3 = 2 + 3 = 5. Step 3: Term 4 = 3 + 5 = 8. Step 4: Term 5 = 5 + 8 = 13. Step 5: Term 6 = 8 + 13 = 21. Step 6: Term 7 = 13 + 21 = 34. Therefore, the 7th term is 34.

Question 10

A series is defined as: 1, 4, 9, 16, 25, ?, 49. What is the missing term?

Accepted Answer

Step 1: Observe each term: 1 = 1², 4 = 2², 9 = 3², 16 = 4², 25 = 5². Step 2: This is a series of perfect squares. Step 3: The missing term should be 6² = 36. Step 4: Verify: 7² = 49 ✓. Therefore, the missing term is 36.

Question 11

A series follows the pattern: 3, 6, 12, 24, ?, 96. What is the missing term?

Accepted Answer

Step 1: Observe the ratio between consecutive terms. 6 ÷ 3 = 2, 12 ÷ 6 = 2, 24 ÷ 12 = 2. Step 2: This is a geometric series with common ratio r = 2. Step 3: The missing term = 24 × 2 = 48. Step 4: Verify: 48 × 2 = 96 ✓. Therefore, the missing term is 48.

Question 12

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 13

In a series, each term is formed by the formula aₙ = n(n+1)(n+2)/6. The series is 1, 4, 10, 20, 35, ... What is the value of a₇?

Accepted Answer

Step 1: Recognize that aₙ = n(n+1)(n+2)/6 is the formula for tetrahedral numbers. Step 2: For n = 7: a₇ = 7 × 8 × 9 / 6. Step 3: Calculate: 7 × 8 = 56; 56 × 9 = 504. Step 4: Divide by 6: 504 / 6 = 84. Therefore, the answer is 84.

Question 14

A number series follows the pattern where each term is obtained by multiplying the previous term by a constant and then adding a fixed value. If the series is 5, 13, 29, 61, 125, ?, what is the next term?

Accepted Answer

Step 1: Find the pattern by examining differences and ratios. Step 2: 5 × 2 + 3 = 13; 13 × 2 + 3 = 29; 29 × 2 + 3 = 61; 61 × 2 + 3 = 125. Step 3: Apply the same rule: 125 × 2 + 3 = 253. Therefore, the answer is 253.

Question 15

In a series, the nth term is defined as n² + 4n + 3. If we list the terms for n = 1, 2, 3, 4, 5, ..., what is the difference between the 8th term and the 6th term?

Accepted Answer

Step 1: Find the 8th term using the formula: 8² + 4(8) + 3 = 64 + 32 + 3 = 99. Step 2: Find the 6th term: 6² + 4(6) + 3 = 36 + 24 + 3 = 63. Step 3: Calculate the difference: 99 - 63 = 36. Therefore, the answer is 36.

Question 16

A series is constructed as follows: the first term is 2, and each subsequent term is the sum of all previous terms plus 1. What is the 5th term of this series?

Accepted Answer

Step 1: Term 1 = 2. Step 2: Term 2 = (sum of previous terms) + 1 = 2 + 1 = 3. Step 3: Term 3 = (2 + 3) + 1 = 6. Step 4: Term 4 = (2 + 3 + 6) + 1 = 12. Step 5: Term 5 = (2 + 3 + 6 + 12) + 1 = 24. Therefore, the answer is 24.

Question 17

A number series has the property that the difference between consecutive terms follows the pattern 3, 6, 12, 24, ... (each difference is double the previous). If the first term is 5, what is the 5th term?

Accepted Answer

Step 1: Term 1 = 5. Step 2: Difference between Term 1 and Term 2 is 3, so Term 2 = 5 + 3 = 8. Step 3: Difference between Term 2 and Term 3 is 6, so Term 3 = 8 + 6 = 14. Step 4: Difference between Term 3 and Term 4 is 12, so Term 4 = 14 + 12 = 26. Step 5: Difference between Term 4 and Term 5 is 24, so Term 5 = 26 + 24 = 50. Therefore, the answer is 50.

SSC GD Constable Number Series

Number Series— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Number Series — Practice Questions

60-Second Revision — Number Series