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Number Series - Advanced Level: fraction series ADVANCED

Master number series concepts through this hard problem set practice set. Worksheet 26 of 30 contains 20 advanced-level problems. Deep dive into fraction series while learning cube series, fibonacci patterns, prime series. Recommended for advanced learners aiming for complex scenarios and multi-step problems.

📝 Worksheet 26 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Number Series
Worksheet 26 of 30 (86% complete)

Question 1

Find the next term in the series: 8, 27, 64, 125, 216, ?
This is a series of consecutive perfect cubes: 2³, 3³, 4³... Next term = 7³ = 343
perfect, cubes

Question 2

Find the next term in the series: 5, 12, 8, 36, 11, 108, 14, 324, ?
Alternating series: First: +3, Second: ×3. Next follows second pattern: 14 × 3 = 42
alternating, arithmetic

Question 3

Find the next term in the series: 4, 6, 5, 15, 26, ?
This is a Tribonacci series where each term is the sum of the previous three terms. Next term = 26 + 15 + 5 = 46
fibonacci, recursive

Question 4

Find the next term in the series: 2, 6, 24, 120, ?
This is a factorial series: 2!, 3!, 4!... Next term = 6! = 720
factorial, growth

Question 5

Find the next term in the series: 7, 15, 10, 45, 13, 135, 16, 405, ?
Alternating series: First: +3, Second: ×3. Next follows second pattern: 16 × 3 = 48
alternating, arithmetic

Question 6

Find the next term in the series: 20, 22, 24, 26, ?
This is an arithmetic series with common difference 2. Next term = 26 + 2 = 28
arithmetic, progression

Question 7

Find the next term in the series: 3/6, 3/7, 3/8, 3/9, 3/10, 3/11, ?
The denominator increases by 1 each time while numerator remains 3. Next term = 3/12
fraction, pattern

Question 8

Find the next term in the series: 8, 16, 32, 64, 128, ?
This is an exponential series with base 2: 2^3, 2^4, 2^5... Next term = 2^8 = 256
exponential, growth

Question 9

Find the next term in the series: 63, 124, 215, 342, ?
This is a series of consecutive perfect cubes minus 1: (4³-1), (5³-1)... Next term = 8³ - 1 = 511
perfect, cubes

Question 10

Find the next term in the series: 24, 61, 122, 213, 340, ?
This is a series of consecutive perfect cubes minus 3: (3³-3), (4³-3)... Next term = 8³ - 3 = 509
perfect, cubes

Question 11

Find the next term in the series: 1, 4, 9, 16, 25, 36, ?
This is a series of consecutive perfect squares: 1², 2², 3²... Next term = 7² = 49
perfect, squares

Question 12

Find the next term in the series: 2, 7, 4, 14, 8, 28, 16, 56, ?
Two alternating geometric series: First: ×2, Second: ×2. Next follows second pattern: 16 × 2 = 32
alternating, arithmetic

Question 13

Find the next term in the series: 4, 8, 16, 32, ?
This is a geometric series with common ratio 2. Next term = 32 × 2 = 64
geometric, progression

Question 14

Find the next term in the series: 101, 103, 107, 109, 113, ?
This is a series of consecutive prime numbers. The next prime after 113 is 127
prime, numbers

Question 15

Find the next term in the series: 2/4, 3/5, 4/6, 5/7, 6/8, 7/9, ?
Both numerator and denominator increase by 1 each time. Next term = 8/10
fraction, pattern

Question 16

Find the next term in the series: 7, 11, 17, 25, 35, ?
The differences between terms increase by 2 each time. Last difference was 10, next difference is 12, so next term = 35 + 12 = 47
difference, pattern

Question 17

Find the next term in the series: 2, 6, 24, 120, 720, ?
This is a factorial series: 2!, 3!, 4!... Next term = 7! = 5040
factorial, growth

Question 18

Find the next term in the series: 15, 30, 15, 30, 15, ?
Alternating series: multiply by 2, divide by 2. Next operation gives 30
alternating, operations

Question 19

Find the next term in the series: 6, 12, 24, 48, 96, ?
This is a geometric series with common ratio 2. Next term = 96 × 2 = 192
geometric, progression

Question 20

Find the next term in the series: 1, 8, 9, 17, 26, 43, ?
Each term is the sum of the previous two terms. Next term = 43 + 26 = 69
fibonacci, recursive
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