To solve the problem, we need to identify the pattern or rule governing each number sequence and then use that rule to fill in the missing numbers. Let's go through each sequence step by step.
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1) 5, 10, 20, __, __, __, __
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Rule: Each term is multiplied by 2.
- \( 5 \times 2 = 10 \)
- \( 10 \times 2 = 20 \)
- \( 20 \times 2 = 40 \)
- \( 40 \times 2 = 80 \)
- \( 80 \times 2 = 160 \)
- \( 160 \times 2 = 320 \)
Sequence: 5, 10, 20, 40, 80, 160, 320
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2) -10, -25, -40, __, __, __, __
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Rule: Each term decreases by 15.
- \( -10 - 15 = -25 \)
- \( -25 - 15 = -40 \)
- \( -40 - 15 = -55 \)
- \( -55 - 15 = -70 \)
- \( -70 - 15 = -85 \)
- \( -85 - 15 = -100 \)
Sequence: -10, -25, -40, -55, -70, -85, -100
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3) 99, 91, 83, __, __, __, __
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Rule: Each term decreases by 8.
- \( 99 - 8 = 91 \)
- \( 91 - 8 = 83 \)
- \( 83 - 8 = 75 \)
- \( 75 - 8 = 67 \)
- \( 67 - 8 = 59 \)
- \( 59 - 8 = 51 \)
Sequence: 99, 91, 83, 75, 67, 59, 51
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4) 0.7, 0.9, 1.1, __, __, __, __
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Rule: Each term increases by 0.2.
- \( 0.7 + 0.2 = 0.9 \)
- \( 0.9 + 0.2 = 1.1 \)
- \( 1.1 + 0.2 = 1.3 \)
- \( 1.3 + 0.2 = 1.5 \)
- \( 1.5 + 0.2 = 1.7 \)
- \( 1.7 + 0.2 = 1.9 \)
Sequence: 0.7, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9
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5) 6.4, 6.9, 7.4, __, __, __, __
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Rule: Each term increases by 0.5.
- \( 6.4 + 0.5 = 6.9 \)
- \( 6.9 + 0.5 = 7.4 \)
- \( 7.4 + 0.5 = 7.9 \)
- \( 7.9 + 0.5 = 8.4 \)
- \( 8.4 + 0.5 = 8.9 \)
- \( 8.9 + 0.5 = 9.4 \)
Sequence: 6.4, 6.9, 7.4, 7.9, 8.4, 8.9, 9.4
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6) -52, -43, __, __, __, __
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Rule: Each term increases by 9.
- \( -52 + 9 = -43 \)
- \( -43 + 9 = -34 \)
- \( -34 + 9 = -25 \)
- \( -25 + 9 = -16 \)
- \( -16 + 9 = -7 \)
- \( -7 + 9 = 2 \)
Sequence: -52, -43, -34, -25, -16, -7, 2
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7) 420, 470, 520, __, __, __, __
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Rule: Each term increases by 50.
- \( 420 + 50 = 470 \)
- \( 470 + 50 = 520 \)
- \( 520 + 50 = 570 \)
- \( 570 + 50 = 620 \)
- \( 620 + 50 = 670 \)
- \( 670 + 50 = 720 \)
Sequence: 420, 470, 520, 570, 620, 670, 720
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8) 26, 66, 106, __, __, __, __
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Rule: Each term increases by 40.
- \( 26 + 40 = 66 \)
- \( 66 + 40 = 106 \)
- \( 106 + 40 = 146 \)
- \( 146 + 40 = 186 \)
- \( 186 + 40 = 226 \)
- \( 226 + 40 = 266 \)
Sequence: 26, 66, 106, 146, 186, 226, 266
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9) -3, -12, -21, __, __, __, __
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Rule: Each term decreases by 9.
- \( -3 - 9 = -12 \)
- \( -12 - 9 = -21 \)
- \( -21 - 9 = -30 \)
- \( -30 - 9 = -39 \)
- \( -39 - 9 = -48 \)
- \( -48 - 9 = -57 \)
Sequence: -3, -12, -21, -30, -39, -48, -57
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10) 2, 6, 18, __, __, __, __
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Rule: Each term is multiplied by 3.
- \( 2 \times 3 = 6 \)
- \( 6 \times 3 = 18 \)
- \( 18 \times 3 = 54 \)
- \( 54 \times 3 = 162 \)
- \( 162 \times 3 = 486 \)
- \( 486 \times 3 = 1458 \)
Sequence: 2, 6, 18, 54, 162, 486, 1458
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Final Answer
\[
\boxed{
\begin{array}{ll}
1) & 5, 10, 20, 40, 80, 160, 320 \\
2) & -10, -25, -40, -55, -70, -85, -100 \\
3) & 99, 91, 83, 75, 67, 59, 51 \\
4) & 0.7, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9 \\
5) & 6.4, 6.9, 7.4, 7.9, 8.4, 8.9, 9.4 \\
6) & -52, -43, -34, -25, -16, -7, 2 \\
7) & 420, 470, 520, 570, 620, 670, 720 \\
8) & 26, 66, 106, 146, 186, 226, 266 \\
9) & -3, -12, -21, -30, -39, -48, -57 \\
10) & 2, 6, 18, 54, 162, 486, 1458 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of sequences worksheet year 7.
