Change in Arithmetic and Geometric Sequences
Two step rules generate the unit. An arithmetic sequence adds a constant difference each step and grows along a line. A geometric sequence multiplies by a constant ratio each step and grows along an exponential curve. Both come in explicit form (jump to term n in one evaluation) and recursive form (take one step at a time), and the subscript in either is a step count, not a decoration.
The mistakes are two: treating multiplicative growth as if it added a fixed amount, and losing count of steps, using n steps where the sequence starts at term 1 and only n - 1 steps have been taken. Both are named and drilled in the lesson.
The work
3 ways in · any order
Lesson
Change in Arithmetic and Geometric Sequences
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Constant difference or constant ratio: the lesson separates the two step rules, connects explicit and recursive forms, and drills the indexing discipline that keeps exponents honest. Ten scenarios close it out: identify, extend, and jump to distant terms of both families.
Diagnostic
10-item topic check
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Ten items spanning the two Topic 2.1 misconceptions: extending a constant-ratio pattern additively, and off-by-one step counts between explicit and recursive forms. The bank ships with the Unit 2 data drop.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.