KKhaemenes PrecalculusTeacher Answer Key
Student Lesson

Teacher Key · Unit 10 · Lesson 01

Sequences, Recursive Definitions & Explicit Rules

Use this key to verify method, notation, domain, units, and interpretation. Accept equivalent exact forms when mathematically valid.

Khaemenes Academy · Teacher Key

Sequences, Recursive Definitions & Explicit Rules

U10 · L01
1

Find the next term: 4,9,14,19,…

Sequences visualModel discrete change with explicit and recursive sequences, arithmetic and geometric patterns, and finite or infinite series. xy
Answer: 24
Reasoning: Common difference is 5.
2

Write an explicit rule for 4,9,14,…

Sequences visualModel discrete change with explicit and recursive sequences, arithmetic and geometric patterns, and finite or infinite series. xy
Answer: a_n=4+5(n−1)
Reasoning: Arithmetic sequence.
3

Find a_8 for a_n=3·2^{n−1}.

Sequences visualModel discrete change with explicit and recursive sequences, arithmetic and geometric patterns, and finite or infinite series. xy
Answer: 384
Reasoning: 3·2⁷=384.
4

Give a recursive rule for 10,7,4,1,…

Sequences visualModel discrete change with explicit and recursive sequences, arithmetic and geometric patterns, and finite or infinite series. xy
Answer: a₁=10; a_n=a_{n−1}−3
Reasoning: Subtract 3 each step.
5

Is 2,6,18,54 arithmetic or geometric?

Sequences visualModel discrete change with explicit and recursive sequences, arithmetic and geometric patterns, and finite or infinite series. xy
Answer: Geometric
Reasoning: Common ratio is 3.
6

Find the 20th term of a_n=7+4(n−1).

Sequences visualModel discrete change with explicit and recursive sequences, arithmetic and geometric patterns, and finite or infinite series. xy
Answer: 83
Reasoning: 7+4·19=83.
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