What is a mixed sequence?
A mixed sequence is a sequence of numbers where the pattern involves more than one type of operation—often a combination of arithmetic (addition/subtraction) and geometric (multiplication/division) patterns.
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Unlike arithmetic or geometric sequences, the rule changes or alternates.
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You need to identify the pattern carefully to continue the sequence.
Step 1: Identify the pattern
Look at the differences or ratios between consecutive terms:
Example 1: Alternating arithmetic and geometric pattern
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Step 1: Compare terms:
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2 → 4 (×2)
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4 → 5 (+1)
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5 → 10 (×2)
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10 → 11 (+1)
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11 → 22 (×2)
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✅ Pattern: multiply by 2, then add 1, repeatedly
Step 2: Predict the next terms
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Using the pattern
(×2, +1):
✅ Next three terms: 23, 46, 47
Step 3: Other types of mixed sequences
Example 2: Arithmetic-geometric sequence
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Pattern: multiply by 2, then add 1
Example 3: Alternating signs or subtraction/addition
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Pattern: multiply by -2 each time
Step 4: How to solve mixed sequence problems
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List the terms and check the difference or ratio between consecutive terms.
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Look for alternating or repeating patterns.
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Test your rule by applying it to all given terms.
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Use your rule to predict future terms.
Step 5: Real-life examples
| Scenario | Sequence | Pattern |
|---|---|---|
| Population with alternating growth and migration | 100, 150, 140, 210, 200… | ×1.5, -10 |
| Investment with interest and withdrawal | 1000, 1200, 1150, 1380… | +20%, -50 |
| Alternating steps in a staircase | 1, 2, 4, 5, 10, 11… | ×2, +1 |
Common beginner mistakes
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❌ Assuming it’s purely arithmetic or geometric
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❌ Missing the alternating operation
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❌ Not testing the pattern on all terms
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❌ Forgetting signs (+/-) in the pattern
Summary
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Mixed sequences = combination of arithmetic and geometric operations (or other alternating rules)
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Carefully identify the pattern
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Predict future terms using the identified rule
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Useful in complex patterns in math, science, and finance