Review of Sequences

Learning Objectives Identify the rule in an arithmetic or geometric sequence. Use a loop with a variable to generate a sequence. Predict the next three terms in a given sequence. Create a sequence that follows a rule involving two operations (e.g., multiply by 2, then add 1). Describe a sequence using computer science terms like 'initial value', 'step', and 'iteration'. Differentiate between arithmetic and geometric sequences. Ever notice how your favorite video game levels get harder in a predictable way? 🎮 That's all about sequences! We're going to review sequences, which are ordered lists of numbers or objects that follow a specific rule. Understanding them helps us create powerful loops in our code and predict patterns in games a...

TermDefinitionExample SequenceAn ordered list of items, like numbers or instructions, that follow a specific rule.The list `2, 4, 6, 8, 10` is a sequence where you add 2 each time. TermA single item or number in a sequence.In the sequence `5, 10, 15, 20`, the number `15` is the third term. RuleThe pattern or instruction you follow to get from one term to the next.For the sequence `3, 6, 9, 12`, the rule is 'add 3'. Arithmetic SequenceA sequence where you add or subtract the same number each time to get to the next term.The sequence `10, 8, 6, 4, 2` is arithmetic because the rule is 'subtract 2'. Geometric SequenceA sequence where you multiply or divide by the same number each time to get to the next term.The sequence `2, 4, 8, 16, 32` is geometric because the rule is &...

The `for` Loop Pattern for Sequences FOR variable FROM start TO end STEP amount Use this pattern to generate sequences in code. `start` is the first term, `end` is the limit, and `amount` is the number you add or subtract each time (the rule for an arithmetic sequence). Finding the Rule Next Term - Current Term (Arithmetic) OR Next Term / Current Term (Geometric) To find a sequence's rule, first try subtracting a term from the one after it. If the result is always the same, the sequence is arithmetic. If not, try dividing. If that result is always the same, it's geometric. The 'Growing' Loop Variable variable = variable * multiplier OR variable = variable + amount Inside a loop, you can make a variable change according to a sequence rule. This is...