Number Patterns - Number Series - One Worksheet / FREE Printable - Free Printable

To solve the problem of identifying number patterns and filling in the missing numbers, we need to analyze each sequence individually and determine the rule governing the pattern. Let's go through each sequence step by step:

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1) Sequence: 2, 3, 5, 8, 12, __, __, __

- Pattern Analysis:
- The differences between consecutive terms are:
- \(3 - 2 = 1\)
- \(5 - 3 = 2\)
- \(8 - 5 = 3\)
- \(12 - 8 = 4\)
- The differences increase by 1 each time.
- Next Terms:
- Next difference: \(4 + 1 = 5\)
- \(12 + 5 = 17\)
- Next difference: \(5 + 1 = 6\)
- \(17 + 6 = 23\)
- Next difference: \(6 + 1 = 7\)
- \(23 + 7 = 30\)
- Completed Sequence: \(2, 3, 5, 8, 12, 17, 23, 30\)

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2) Sequence: 5, 7, 11, 17, 25, __, __, __

- Pattern Analysis:
- The differences between consecutive terms are:
- \(7 - 5 = 2\)
- \(11 - 7 = 4\)
- \(17 - 11 = 6\)
- \(25 - 17 = 8\)
- The differences increase by 2 each time.
- Next Terms:
- Next difference: \(8 + 2 = 10\)
- \(25 + 10 = 35\)
- Next difference: \(10 + 2 = 12\)
- \(35 + 12 = 47\)
- Next difference: \(12 + 2 = 14\)
- \(47 + 14 = 61\)
- Completed Sequence: \(5, 7, 11, 17, 25, 35, 47, 61\)

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3) Sequence: 48, 47, 45, 42, 38, __, __, __

- Pattern Analysis:
- The differences between consecutive terms are:
- \(47 - 48 = -1\)
- \(45 - 47 = -2\)
- \(42 - 45 = -3\)
- \(38 - 42 = -4\)
- The differences decrease by 1 each time (or increase by -1).
- Next Terms:
- Next difference: \(-4 - 1 = -5\)
- \(38 - 5 = 33\)
- Next difference: \(-5 - 1 = -6\)
- \(33 - 6 = 27\)
- Next difference: \(-6 - 1 = -7\)
- \(27 - 7 = 20\)
- Completed Sequence: \(48, 47, 45, 42, 38, 33, 27, 20\)

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4) Sequence: 101, 90, 80, 71, 63, __, __, __

- Pattern Analysis:
- The differences between consecutive terms are:
- \(90 - 101 = -11\)
- \(80 - 90 = -10\)
- \(71 - 80 = -9\)
- \(63 - 71 = -8\)
- The differences increase by 1 each time (or decrease by -1).
- Next Terms:
- Next difference: \(-8 + 1 = -7\)
- \(63 - 7 = 56\)
- Next difference: \(-7 + 1 = -6\)
- \(56 - 6 = 50\)
- Next difference: \(-6 + 1 = -5\)
- \(50 - 5 = 45\)
- Completed Sequence: \(101, 90, 80, 71, 63, 56, 50, 45\)

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5) Sequence: 3, 7, 12, 18, 25, __, __, __

- Pattern Analysis:
- The differences between consecutive terms are:
- \(7 - 3 = 4\)
- \(12 - 7 = 5\)
- \(18 - 12 = 6\)
- \(25 - 18 = 7\)
- The differences increase by 1 each time.
- Next Terms:
- Next difference: \(7 + 1 = 8\)
- \(25 + 8 = 33\)
- Next difference: \(8 + 1 = 9\)
- \(33 + 9 = 42\)
- Next difference: \(9 + 1 = 10\)
- \(42 + 10 = 52\)
- Completed Sequence: \(3, 7, 12, 18, 25, 33, 42, 52\)

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6) Sequence: 79, 77, 74, 70, 65, __, __, __

- Pattern Analysis:
- The differences between consecutive terms are:
- \(77 - 79 = -2\)
- \(74 - 77 = -3\)
- \(70 - 74 = -4\)
- \(65 - 70 = -5\)
- The differences decrease by 1 each time (or increase by -1).
- Next Terms:
- Next difference: \(-5 - 1 = -6\)
- \(65 - 6 = 59\)
- Next difference: \(-6 - 1 = -7\)
- \(59 - 7 = 52\)
- Next difference: \(-7 - 1 = -8\)
- \(52 - 8 = 44\)
- Completed Sequence: \(79, 77, 74, 70, 65, 59, 52, 44\)

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7) Sequence: 8, 9, 11, 14, 18, __, __, __

- Pattern Analysis:
- The differences between consecutive terms are:
- \(9 - 8 = 1\)
- \(11 - 9 = 2\)
- \(14 - 11 = 3\)
- \(18 - 14 = 4\)
- The differences increase by 1 each time.
- Next Terms:
- Next difference: \(4 + 1 = 5\)
- \(18 + 5 = 23\)
- Next difference: \(5 + 1 = 6\)
- \(23 + 6 = 29\)
- Next difference: \(6 + 1 = 7\)
- \(29 + 7 = 36\)
- Completed Sequence: \(8, 9, 11, 14, 18, 23, 29, 36\)

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8) Sequence: 65, 62, 58, 53, 47, __, __, __

- Pattern Analysis:
- The differences between consecutive terms are:
- \(62 - 65 = -3\)
- \(58 - 62 = -4\)
- \(53 - 58 = -5\)
- \(47 - 53 = -6\)
- The differences decrease by 1 each time (or increase by -1).
- Next Terms:
- Next difference: \(-6 - 1 = -7\)
- \(47 - 7 = 40\)
- Next difference: \(-7 - 1 = -8\)
- \(40 - 8 = 32\)
- Next difference: \(-8 - 1 = -9\)
- \(32 - 9 = 23\)
- Completed Sequence: \(65, 62, 58, 53, 47, 40, 32, 23\)

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9) Sequence: 9, 13, 18, 24, 31, __, __, __

- Pattern Analysis:
- The differences between consecutive terms are:
- \(13 - 9 = 4\)
- \(18 - 13 = 5\)
- \(24 - 18 = 6\)
- \(31 - 24 = 7\)
- The differences increase by 1 each time.
- Next Terms:
- Next difference: \(7 + 1 = 8\)
- \(31 + 8 = 39\)
- Next difference: \(8 + 1 = 9\)
- \(39 + 9 = 48\)
- Next difference: \(9 + 1 = 10\)
- \(48 + 10 = 58\)
- Completed Sequence: \(9, 13, 18, 24, 31, 39, 48, 58\)

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10) Sequence: 13, 14, 16, 19, 23, __, __, __

- Pattern Analysis:
- The differences between consecutive terms are:
- \(14 - 13 = 1\)
- \(16 - 14 = 2\)
- \(19 - 16 = 3\)
- \(23 - 19 = 4\)
- The differences increase by 1 each time.
- Next Terms:
- Next difference: \(4 + 1 = 5\)
- \(23 + 5 = 28\)
- Next difference: \(5 + 1 = 6\)
- \(28 + 6 = 34\)
- Next difference: \(6 + 1 = 7\)
- \(34 + 7 = 41\)
- Completed Sequence: \(13, 14, 16, 19, 23, 28, 34, 41\)

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Final Answer

\[
\boxed{
\begin{array}{l}
1) \ 2, 3, 5, 8, 12, 17, 23, 30 \\
2) \ 5, 7, 11, 17, 25, 35, 47, 61 \\
3) \ 48, 47, 45, 42, 38, 33, 27, 20 \\
4) \ 101, 90, 80, 71, 63, 56, 50, 45 \\
5) \ 3, 7, 12, 18, 25, 33, 42, 52 \\
6) \ 79, 77, 74, 70, 65, 59, 52, 44 \\
7) \ 8, 9, 11, 14, 18, 23, 29, 36 \\
8) \ 65, 62, 58, 53, 47, 40, 32, 23 \\
9) \ 9, 13, 18, 24, 31, 39, 48, 58 \\
10) \ 13, 14, 16, 19, 23, 28, 34, 41 \\
\end{array}
}
\]