LEARN · EXPLAIN · REVISE

Find the smallest positive index with an>t.

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

高二選擇性必修第二册(A版).pdf · 4.1 · PDF 7 / printed page 2

TOPIC 01

Concept of a sequence

Connect general terms, recurrence relations and partial sums.

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

01 / Standard#Your turn

a_n=2n-1,\quad t=10

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Express the indexed terms or partial sums before simplifying.

Hint 2

Use this intermediate relation.

2n-1>t

Worked solution

The requested value is 6.

Checks and common pitfalls: A strict inequality and an integer index require the next larger integer.

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

Teacher preparation and assessment

Defining relation: Connect general terms, recurrence relations and partial sums.
$a_n=S_n-S_{n-1}\ (n\ge2)$
Conditions: Indices are positive integers; a1=S1 needs separate treatment.