Change in Arithmetic and Geometric Sequences
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalTwo 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 the exponent one less than the term number. 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. Results route you to the drills that fix what fired.
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 it for now and moves you to the next. Two in a row is a checkpoint, not proof: if the error resurfaces later, the misconception comes back.