LEARN · EXPLAIN · REVISE

Find a1.

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 / Foundation#Your turn

S_n=n^2+7\quad(n\ge1)

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.

a_1=S_1

Worked solution

Express the indexed terms or partial sums before simplifying.
Apply the stated relation and retain its conditions.
$a_1=1^2+7=8$
The formula was not given at n=0; subtracting its extrapolated S0 would lose the constant.

The requested value is 8.

Checks and common pitfalls: The formula was not given at n=0; subtracting its extrapolated S0 would lose the constant.

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.