Question 1

Complete the series: 1, 4, 9, 16, 25, ?, 49

Accepted Answer

Step 1: Recognize these are perfect squares. 1=1², 4=2², 9=3², 16=4², 25=5², 49=7². Step 2: The series is n² where n = 1, 2, 3, 4, 5, ?, 7. Step 3: Missing value of n = 6. Step 4: Missing term = 6² = 36.

Question 2

What comes next? 2, 5, 10, 17, 26, ?

Accepted Answer

Step 1: Calculate first differences: 5−2=3, 10−5=5, 17−10=7, 26−17=9. Step 2: First differences are 3, 5, 7, 9 (odd numbers increasing by 2). Step 3: Next first difference = 11. Step 4: Next term = 26 + 11 = 37.

Question 3

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

Accepted Answer

Step 1: Observe each term. 3 = 3¹, 9 = 3², 27 = 3³, 81 = 3⁴. Step 2: This is a geometric series with common ratio r = 3. Step 3: Next term = 81 × 3 = 243 = 3⁵.

Question 4

Find the missing number in the series: 5, 10, 20, 40, 80, ?

Accepted Answer

Step 1: Identify the pattern by examining the ratio between consecutive terms. Step 2: 10÷5 = 2, 20÷10 = 2, 40÷20 = 2, 80÷40 = 2. Step 3: Each term is multiplied by 2 to get the next term. Step 4: 80 × 2 = 160. Therefore, the missing number is 160.

Question 5

What comes next in the series: 2, 3, 5, 8, 13, ___?

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. Step 2: This is a Fibonacci-type series. Step 3: Next term = 8 + 13 = 21.

Question 6

Find the missing number in the series: 2, 6, 12, 20, 30, ?, 56

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 should be 12. Step 4: Missing number = 30 + 12 = 42. Step 5: Verify: 42 + 14 = 56 ✓

Question 7

Find the next number: 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 each time). Step 3: Next term = 12.5 × 0.5 = 6.25.

Question 8

What is the next number in the series: 1, 4, 9, 16, 25, ?

Accepted Answer

Step 1: Recognize that each term is a perfect square: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25. Step 2: The series represents the squares of consecutive natural numbers. Step 3: The next natural number is 6. Step 4: 6² = 36. Therefore, the missing number is 36.

Question 9

Complete the series: 1, 4, 9, 16, 25, ___

Accepted Answer

Step 1: Recognize that each term is a perfect square: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25. Step 2: The series represents n² where n = 1, 2, 3, 4, 5, ... Step 3: The next term is 6² = 36.

Question 10

Find the missing term: 3, 9, 27, 81, ?

Accepted Answer

Step 1: Examine the relationship between consecutive terms. Step 2: 9÷3 = 3, 27÷9 = 3, 81÷27 = 3. Step 3: This is a geometric sequence with common ratio 3. Step 4: Each term equals 3 raised to successive powers: 3¹, 3², 3³, 3⁴, 3⁵. Step 5: 81 × 3 = 243 or 3⁵ = 243. Therefore, the missing number is 243.

Question 11

Find the next number in the series: 100, 50, 25, 12.5, ___

Accepted Answer

Step 1: Calculate 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 × 0.5 = 6.25.

Question 12

Find the missing number: 3, 8, 15, 24, 35, ___

Accepted Answer

Step 1: Calculate first differences: 8−3=5, 15−8=7, 24−15=9, 35−24=11. Step 2: The first differences are 5, 7, 9, 11 (arithmetic sequence with common difference 2). Step 3: Next first difference = 11 + 2 = 13. Step 4: Missing term = 35 + 13 = 48.

Question 13

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 14

Find the missing number in the series: 2, 6, 12, 20, 30, ___

Accepted Answer

Step 1: Observe the differences between consecutive terms: 6−2=4, 12−6=6, 20−12=8, 30−20=10. Step 2: The differences form an arithmetic sequence: 4, 6, 8, 10, ... (increasing by 2 each time). Step 3: The next difference should be 12. Step 4: Therefore, the next term = 30 + 12 = 42.

Question 15

Find the missing term: 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 16

What is the next term in the series: 2, 6, 12, 20, 30, ?

Accepted Answer

Step 1: Find the differences between consecutive terms: 6−2=4, 12−6=6, 20−12=8, 30−20=10. Step 2: The first differences form the sequence 4, 6, 8, 10 (increasing by 2 each time). Step 3: The next first difference should be 12. Step 4: 30 + 12 = 42. Therefore, the missing number is 42.

Question 17

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: Each subsequent difference increases by 1. So differences are: 1, 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 18

A series is constructed where each term is the product of its position and the sum of all previous terms. If the first term is 2, what is the 4th term?

Accepted Answer

Step 1: Term 1 = 2. Sum of previous terms = 0. Step 2: Term 2 = 2 × (0 + 2) = 2 × 2 = 4. Sum so far = 2 + 4 = 6. Step 3: Term 3 = 3 × (2 + 4) = 3 × 6 = 18. Sum so far = 2 + 4 + 18 = 24. Step 4: Term 4 = 4 × (2 + 4 + 18) = 4 × 24 = 96. Therefore, the 4th term is 96.

Question 19

In a series, the difference between consecutive terms increases by 1 each time. If the first term is 3 and the second term is 4, what is the 6th term?

Accepted Answer

Step 1: Term 1 = 3, Term 2 = 4. The difference is 4 − 3 = 1. Step 2: Term 3 = 4 + 2 = 6 (difference increases to 2). Step 3: Term 4 = 6 + 3 = 9 (difference increases to 3). Step 4: Term 5 = 9 + 4 = 13 (difference increases to 4). Step 5: Term 6 = 13 + 5 = 18 (difference increases to 5). Therefore, the 6th term is 18.

Question 20

A series is defined as: 2, 6, 12, 20, 30, ... What is the 8th term of this series?

Accepted Answer

Step 1: Observe the pattern. Term 1 = 2 = 1×2, Term 2 = 6 = 2×3, Term 3 = 12 = 3×4, Term 4 = 20 = 4×5, Term 5 = 30 = 5×6. Step 2: The nth term follows T(n) = n(n+1). Step 3: For the 8th term, T(8) = 8 × 9 = 72. Therefore, the 8th term is 72.

RRB NTPC Number Series

Number Series— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Number Series — Practice Questions

60-Second Revision — Number Series