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Arithmetic Sequence Sum

等差数列前n项和公式

Sn​=2n(a1​+an​)​

Theoretical Identity Description:

Finds the sum of the first n terms of an arithmetic sequence. Represents the sum of terms multiplied by their average.

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Rigorous Derivation Tree

2 Logical Steps
Step 1check_circleValid Deduction
Sn​=2n(a1​+an​)​

Foundational identity statement defined under standard mathematical conditions.

Step 2check_circleValid Deduction
Sn​=2n(a1​+an​)​

Targeted algebraic evaluation and parameter substitution.

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CSCA Exam Triggers & Traps

High-Yield Exam Focus
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Apply whenever an exam question presents conditions matching this canonical identity.

errorCommon Examination Pitfalls

Be vigilant of domain boundaries, sign flips, and degenerate boundary condition cases.

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Related Formulas in Sequences

4 Formulas
Arithmetic Sequence Nth Term
等差数列通项公式
Arithmetic Sequence Sum
等差数列前n项和公式
Geometric Sequence Nth Term
等比数列通项公式
Geometric Sequence Sum
等比数列前n项和公式

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