LEARN · EXPLAIN · REVISE

How many terms of 2,5,8,… are at most 3t+2?

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

高二選擇性必修第二册(A版).pdf · 4.2 · PDF 17 / printed page 12

TOPIC 01

Arithmetic sequences

Derive terms and sums and solve indexed arithmetic models.

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

01 / Standard#Worked example

t=3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use the common difference and the arithmetic-sum formula.

Hint 2

Use this intermediate relation.

2+3(n-1)\le3t+2

Worked solution

The requested value is 4.

Checks and common pitfalls: The inclusive endpoint is counted.

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

Teacher preparation and assessment

Defining relation: Derive terms and sums and solve indexed arithmetic models.
$a_n=a_1+(n-1)d;\quad S_n=n(a_1+a_n)/2$
Conditions: A finite sum contains n terms, hence n−1 differences.