Kenneth ChengMathematical modeling
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Find S3.

Read the idea, work independently, then explain what changed.

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TOPIC 01

Sequences: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

What you will be able to explain

  • Connect the chapter skills without relying on the order of the exercises.

Try it. Leave your reasoning visible.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

Find S3.

a1=22,q=3a_1=22,\quad q=3
  • The geometric ratio is defined for nonzero terms; q=1 uses Sn=na1.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Use the common ratio and check its special cases.
Hint 2
Use this intermediate relation.
S3=a1(1+q+q2)S_3=a_1(1+q+q^2)
Worked solution

  1. Use the common ratio and check its special cases.

  2. Apply the stated relation and retain its conditions.

    S3=22(1+3+9)=286S_3=22(1+3+9)=286

  3. Direct expansion is an independent check on the finite-sum formula.

The requested value is 286.

Checks and common pitfalls: Direct expansion is an independent check on the finite-sum formula.

Think first. Reveal a hint when the class is ready.

Focus on one question

Teacher preparation and assessment

Question sequence

  • Ask students to name the relevant condition before calculating.

Board plan

  • Compare valid methods and annotate their conditions.

Anticipated thinking

  • A correct final value may still hide a missing assumption.

Assessment checklist

  • Check the method, conditions, reasoning and interpretation separately.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗