Question 1

Find the next 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 answer is 160.

Question 2

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 squares of consecutive natural numbers. Step 3: The next term is 6² = 36. Therefore, the answer is 36.

Question 3

Find the missing number in the series: 100, 90, 81, 73, 66, ?

Accepted Answer

Step 1: Calculate differences between consecutive terms: 100-90=10, 90-81=9, 81-73=8, 73-66=7. Step 2: The differences form a decreasing sequence: 10, 9, 8, 7. Step 3: The next difference should be 6. Step 4: 66 - 6 = 60. Therefore, the answer is 60.

Question 4

What is the missing number in the series: 3, 6, 12, 24, 48, ?

Accepted Answer

Step 1: Observe the relationship between consecutive terms. Step 2: 6÷3=2, 12÷6=2, 24÷12=2, 48÷24=2. Step 3: Each term is multiplied by 2. Step 4: 48 × 2 = 96. Therefore, the answer is 96.

Question 5

Find the next term in the series: 2, 5, 10, 17, 26, ?

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 form a series: 3, 5, 7, 9 (odd numbers increasing by 2). Step 3: The next difference should be 11. Step 4: 26 + 11 = 37. Therefore, the answer is 37.

Question 6

What is the next term in the series: 2, 3, 5, 8, 12, ?

Accepted Answer

Step 1: Find the differences between consecutive terms: 3-2=1, 5-3=2, 8-5=3, 12-8=4. Step 2: The differences form the sequence 1, 2, 3, 4 (consecutive natural numbers). Step 3: The next difference should be 5. Step 4: 12 + 5 = 17. Therefore, the answer is 17.

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

In a series, the nth term is given by the formula: aₙ = n² + 2n − 1. What is the difference between the 5th term and the 3rd term?

Accepted Answer

Step 1: Calculate the 5th term: a₅ = 5² + 2(5) − 1 = 25 + 10 − 1 = 34. Step 2: Calculate the 3rd term: a₃ = 3² + 2(3) − 1 = 9 + 6 − 1 = 14. Step 3: Difference = a₅ − a₃ = 34 − 14 = 20. Therefore, the difference is 20.

Question 9

A series starts with 100 and each term is 80% of the previous term. What is the 4th term of this series (rounded to the nearest integer)?

Accepted Answer

Step 1: Term 1 = 100. Step 2: Term 2 = 100 × 0.8 = 80. Step 3: Term 3 = 80 × 0.8 = 64. Step 4: Term 4 = 64 × 0.8 = 51.2. Step 5: Rounded to nearest integer = 51. Therefore, the 4th term is 51.

Question 10

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: Term 1 = 2, Term 2 = 3. Difference = 1. Step 2: Term 3 = 3 + 2 = 5 (difference increases to 2). Step 3: Term 4 = 5 + 3 = 8 (difference increases to 3). Step 4: Term 5 = 8 + 4 = 12 (difference increases to 4). Step 5: Term 6 = 12 + 5 = 17 (difference increases to 5). Therefore, the 6th term is 17.

Question 11

A series is defined as: 3, 6, 12, 24, 48, ... What is the sum of the 6th and 7th terms of this series?

Accepted Answer

Step 1: Identify the pattern — each term is double the previous term (geometric series with r = 2). Step 2: 6th term = 48 × 2 = 96. Step 3: 7th term = 96 × 2 = 192. Step 4: Sum = 96 + 192 = 288. Therefore, the answer is 288.

Question 12

A number series follows the pattern where each term is the sum of the previous two terms. If the 3rd term is 8 and the 4th term is 13, what is the 1st term?

Accepted Answer

Step 1: Let the 1st term be a and 2nd term be b. Step 2: 3rd term = a + b = 8. Step 3: 4th term = b + (a + b) = a + 2b = 13. Step 4: From equation 1: a = 8 − b. Substitute into equation 2: (8 − b) + 2b = 13, so 8 + b = 13, thus b = 5. Step 5: a = 8 − 5 = 3. Therefore, the 1st term is 3.

Question 13

A series is defined as: a₁ = 2, and a(n) = a(n-1) + n² for n ≥ 2. What is the value of a₆?

Accepted Answer

Step 1: a₁ = 2. Step 2: a₂ = a₁ + 2² = 2 + 4 = 6. Step 3: a₃ = a₂ + 3² = 6 + 9 = 15. Step 4: a₄ = a₃ + 4² = 15 + 16 = 31. Step 5: a₅ = a₄ + 5² = 31 + 25 = 56. Step 6: a₆ = a₅ + 6² = 56 + 36 = 92.

Question 14

A series has the property that each term (starting from the third) is the sum of the two preceding terms multiplied by a constant k. If a₁ = 1, a₂ = 2, a₃ = 9, and a₄ = 33, what is a₅?

Accepted Answer

Step 1: The rule is a(n) = k(a(n-1) + a(n-2)) for n ≥ 3. Step 2: From a₃ = 9: k(a₂ + a₁) = 9 → k(2 + 1) = 9 → 3k = 9 → k = 3. Step 3: Verify with a₄: 3(a₃ + a₂) = 3(9 + 2) = 3(11) = 33. ✓ Step 4: Calculate a₅ = 3(a₄ + a₃) = 3(33 + 9) = 3(42) = 126.

Question 15

In a series, the difference between consecutive terms follows a pattern: 2, 6, 12, 20, 30, ... If the first term is 5, what is the 7th term of the original series?

Accepted Answer

Step 1: The differences are 2, 6, 12, 20, 30. Step 2: These differences themselves follow a pattern. Check second differences: 6-2=4, 12-6=6, 20-12=8, 30-20=10. Step 3: The second differences increase by 2 each time (4, 6, 8, 10, ...). Step 4: The next first difference is 30 + 12 = 42. Step 5: The next first difference after that is 42 + 14 = 56. Step 6: Original series: a₁=5, a₂=5+2=7, a₃=7+6=13, a₄=13+12=25, a₅=25+20=45, a₆=45+30=75, a₇=75+42=117.

Question 16

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 first term is 3, the second term is 7, and the third term is 15, what is the fifth term of this series?

Accepted Answer

Step 1: Identify the pattern. Let the rule be: a(n) = k × a(n-1) + c. Step 2: From a₁ = 3 to a₂ = 7: 3k + c = 7. Step 3: From a₂ = 7 to a₃ = 15: 7k + c = 15. Step 4: Subtract equation 1 from equation 2: 4k = 8, so k = 2. Step 5: Substitute back: 3(2) + c = 7, so c = 1. Step 6: The rule is a(n) = 2 × a(n-1) + 1. Step 7: a₄ = 2(15) + 1 = 31. Step 8: a₅ = 2(31) + 1 = 63.

SSC MTS Number Series

Number Series— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Number Series — Practice Questions

60-Second Revision — Number Series