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Number Series - Intermediate Level: arithmetic progression INTERMEDIATE

Master number series concepts through this excellence pursuit practice set. Worksheet 16 of 30 contains 20 intermediate-level problems. Deep dive into arithmetic progression while learning arithmetic progression, geometric progression, square series. Recommended for mid-level learners aiming for moderate complexity with mixed patterns.

📝 Worksheet 16 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Number Series
Worksheet 16 of 30 (53% complete)

Question 1

Find the next term in the series: 8, 9, 12, 17, 24, 33, ?
The differences between terms increase by 2 each time. Last difference was 9, next difference is 11, so next term = 33 + 11 = 44
difference, pattern

Question 2

Find the next term in the series: 2, 3, 6, 12, 18, 48, 54, 192, ?
Two alternating geometric series: First: ×3, Second: ×4. Next follows second pattern: 54 × 4 = 216
alternating, arithmetic

Question 3

Find the next term in the series: 6, 24, 120, 720, ?
This is a factorial series: 3!, 4!, 5!... Next term = 7! = 5040
factorial, growth

Question 4

Find the next term in the series: 107, 109, 113, 127, 131, ?
This is a series of consecutive prime numbers. The next prime after 131 is 137
prime, numbers

Question 5

Find the next term in the series: 7, 14, 28, 56, 112, ?
This is a geometric series with common ratio 2. Next term = 112 × 2 = 224
geometric, progression

Question 6

Find the next term in the series: 2, 3, 7, 12, 22, 41, 75, ?
This is a Tribonacci series where each term is the sum of the previous three terms. Next term = 75 + 41 + 22 = 138
fibonacci, recursive

Question 7

Find the next term in the series: 3/6, 4/6, 5/6, 6/6, 7/6, ?
The numerators increase by 1 each time while denominator remains 6. Next term = 8/6
fraction, pattern

Question 8

Find the next term in the series: 14, 17, 22, 29, 38, ?
The differences between terms increase by 2 each time. Last difference was 9, next difference is 11, so next term = 38 + 11 = 49
difference, pattern

Question 9

Find the next term in the series: 10, 24, 12, 28, 14, 32, 16, 36, ?
Two alternating arithmetic series: First: +2, Second: +4. Next follows second pattern: 16 + 4 = 20
alternating, arithmetic

Question 10

Find the next term in the series: 2, 4, 8, 16, 32, 64, ?
This is an exponential series with base 2: 2^1, 2^2, 2^3... Next term = 2^7 = 128
exponential, growth

Question 11

Find the next term in the series: 64, 256, 1024, 4096, 16384, ?
This is an exponential series with base 4: 4^3, 4^4, 4^5... Next term = 4^8 = 65536
exponential, growth

Question 12

Find the next term in the series: 8, 5, 1, -2, -1, ?
Alternating series: -3, ÷3. Next operation gives -4
alternating, operations

Question 13

Find the next term in the series: 29, 66, 127, 218, 345, ?
This is a series of consecutive perfect cubes plus 2: (3³+2), (4³+2)... Next term = 8³ + 2 = 514
perfect, cubes

Question 14

Find the next term in the series: 3, 28, 21953, 10579901690178, ?
Each term follows: (previous term)^3 + 1. Next term = 10579901690178^3 + 1 = 1184254098964082509220217082972843519753
multiplication, addition

Question 15

Find the next term in the series: 5, 9, 14, 20, 27, ?
The differences between terms increase by 1 each time. Last difference was 7, next difference is 8, so next term = 27 + 8 = 35
difference, pattern

Question 16

Find the next term in the series: 16, 18, 20, 22, 24, 26, ?
This is an arithmetic series with common difference 2. Next term = 26 + 2 = 28
arithmetic, progression

Question 17

Find the next term in the series: 13, 15, 19, 25, 33, ?
The differences between terms increase by 2 each time. Last difference was 8, next difference is 10, so next term = 33 + 10 = 43
difference, pattern

Question 18

Find the next term in the series: 10, 29, 66, 127, 218, ?
This is a series of consecutive perfect cubes plus 2: (2³+2), (3³+2)... Next term = 7³ + 2 = 345
perfect, cubes

Question 19

Find the next term in the series: 8, 27, 64, 125, ?
This is a series of consecutive perfect cubes: 2³, 3³, 4³... Next term = 6³ = 216
perfect, cubes

Question 20

Find the next term in the series: 292, 303, 313, 323, 333, 343, ?
This is a series of palindromic numbers (numbers that read the same forwards and backwards). The next palindrome after 343 is 353
palindrome, numbers
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