To solve these problems, we need to find a pattern in each sequence and then use that pattern to calculate the specific term requested. All of these are arithmetic sequences, meaning each number increases by the same amount.
The formula to find any term in an arithmetic sequence is:
Term = First Number + (Position - 1) × Difference
Let's break down each problem one by one.
Problem 1:
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Sequence: 16, 20, 24, 28, 32...
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First Number: 16
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Difference: 20 - 16 = 4
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Target: 22nd term
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Calculation:
* Term = 16 + (22 - 1) × 4
* Term = 16 + (21) × 4
* Term = 16 + 84
* Term = 100
Problem 2:
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Sequence: 3, 9, 15, 21, 27...
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First Number: 3
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Difference: 9 - 3 = 6
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Target: 21st term
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Calculation:
* Term = 3 + (21 - 1) × 6
* Term = 3 + (20) × 6
* Term = 3 + 120
* Term = 123
Problem 3:
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Sequence: 2, 4, 6, 8, 10...
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First Number: 2
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Difference: 4 - 2 = 2
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Target: 18th term
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Calculation:
* Term = 2 + (18 - 1) × 2
* Term = 2 + (17) × 2
* Term = 2 + 34
* Term = 36
Problem 4:
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Sequence: 10, 22, 34, 46, 58...
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First Number: 10
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Difference: 22 - 10 = 12
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Target: 19th term
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Calculation:
* Term = 10 + (19 - 1) × 12
* Term = 10 + (18) × 12
* Term = 10 + 216
* Term = 226
Problem 5:
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Sequence: 22, 27, 32, 37, 42...
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First Number: 22
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Difference: 27 - 22 = 5
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Target: 33rd term
*
Calculation:
* Term = 22 + (33 - 1) × 5
* Term = 22 + (32) × 5
* Term = 22 + 160
* Term = 182
Final Answer:
1. 100
2. 123
3. 36
4. 226
5. 182
Parent Tip: Review the logic above to help your child master the concept of sequences worksheet nth term.
