LEARN · EXPLAIN · REVISE

Find S3.

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

高二選擇性必修第二册(A版).pdf · 4.3 · PDF 32 / printed page 27

TOPIC 01

Geometric sequences

Connect ratios, indexed powers and finite geometric sums.

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

01 / Foundation#Your turn

a_1=7,\quad q=3

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.

S_3=a_1(1+q+q^2)

Worked solution

The requested value is 91.

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.

Teacher preparation and assessment

Defining relation: Connect ratios, indexed powers and finite geometric sums.
$a_n=a_1q^{n-1};\quad S_n=a_1(1-q^n)/(1-q)$
Conditions: The geometric ratio is defined for nonzero terms; q=1 uses Sn=na1.