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Grade 5 Math · Level 5, Patterns & Percents

Arithmetic Sequences, nth Terms & Triangular Numbers

How the lesson starts: Arithmetic Sequences, nth Terms & Triangular Numbers

1. Penguin Lanes

   Welcome to Penguin Lanes, the coolest bowling alley around! Pip the penguin has 2 prize tickets after game 1, and wins 3 more every game: 2, 5, 8, 11. Let's study Pip's ticket pattern!

2. The common difference

   Pip's tickets on a number line: 2, 5, 8, 11, 14. Every jump is +3. A list where the jump never changes is an arithmetic sequence. The jump is the common difference. Find it by subtracting a term from the next one.

3. Fill the gaps

   Kai wrote 4, blank, blank, 19, with the same jump each time. From 4 to 19 is 15, and it takes 3 equal jumps. 15 ÷ 3 = 5. So the gaps are 9 and 14! Watch out: 2 gaps means 3 jumps.