Number sequences - Find the Rule

The resource presents an educational challenge for students to express missing number problems algebraically by identifying patterns in number sequences. The objective is to equip students with the ability to discern the underlying rule of a sequence, predict subsequent numbers, and articulate the pattern through a mathematical formula. Each question presents a different sequence, prompting students to apply their analytical skills to uncover the rule that governs the progression of numbers.

For instance, in one sequence starting with the numbers 3, 30, and 300, the rule is to multiply by 10. Students are expected to continue this pattern to produce the next five numbers: 3000, 30,000, 300,000, 3,000,000, and 30,000,000. The formula representing this sequence is simply 10n. Another example features a sequence beginning with 84, 90, and 96, where the rule is to add 6 to the previous number, leading to the next five numbers being 102, 108, 114, 120, and 126, encapsulated by the formula n + 6. Through these exercises, students learn to recognize arithmetic progressions, geometric progressions, and other patterns, enhancing their algebraic thinking and problem-solving abilities.