@prefix concept: <https://w3id.org/kmath/concept/> .
@prefix course: <https://w3id.org/kmath/course/> .
@prefix math: <https://w3id.org/kmath/> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix review_status: <https://w3id.org/kmath/review_status/> .
@prefix scheme: <https://w3id.org/kmath/scheme/> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix textbook_section: <https://w3id.org/kmath/textbook_section/> .

concept:arithmetic_sum_quadratic_form a math:Concept ;
    rdfs:label "등차수열의 합의 이차식 표현"@ko ;
    skos:altLabel "등차수열의 합은 원점을 지나는 이차함수"@ko ;
    skos:broader concept:arithmetic_sequence_sum ;
    skos:definition "첫째항이 a, 공차가 d인 등차수열의 합은 Sₙ = (d/2)n² + (a − d/2)n으로 상수항이 없는 n에 대한 식이며, d ≠ 0이면 n²의 계수의 2배가 공차인 이차식이다. 역으로 수열의 합이 Sₙ = An² + Bn + C(A, B, C는 상수)이면 C = 0일 때 첫째항부터, C ≠ 0일 때 둘째항부터 등차수열을 이룬다."@ko ;
    skos:editorialNote "2026-09-28 GRIP 대수 개념서와 시발점 워크북 대수가 독립된 학습 항목으로 다루는 것을 근거로 추가했다. 도메인 전문가 검토가 필요하다."@ko ;
    skos:inScheme scheme:concepts ;
    skos:prefLabel "sum of an arithmetic sequence as a quadratic in n"@en,
        "등차수열의 합의 이차식 표현"@ko ;
    math:introducedIn course:algebra ;
    math:requires concept:arithmetic_sequence_sum,
        concept:quadratic_function ;
    math:requiresTransitively concept:algebraic_expression,
        concept:arithmetic_sequence,
        concept:arithmetic_sequence_sum,
        concept:coordinate_plane,
        concept:direct_proportion,
        concept:equation,
        concept:exponent_law,
        concept:factorization,
        concept:function,
        concept:graph,
        concept:integer,
        concept:inverse_proportion,
        concept:linear_equation,
        concept:linear_function,
        concept:multiplication_formula,
        concept:polynomial,
        concept:polynomial_operation,
        concept:power,
        concept:quadratic_equation,
        concept:quadratic_function,
        concept:rational_number,
        concept:sequence,
        concept:sequence_sum,
        concept:square_root ;
    math:reviewStatus review_status:needs_review ;
    math:sourceSection textbook_section:grip_algebra_08_07_arithmetic_sum_extremum,
        textbook_section:grip_algebra_08_08_sum_general_term_relation,
        textbook_section:grip_algebra_08_sp2_arithmetic_sum_symmetry,
        textbook_section:sibaljeom_workbook_algebra_theme27_arithmetic_sum_quadratic ;
    math:taughtIn course:algebra .