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MashaKolachuk1503
@MashaKolachuk1503
July 2022
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дано арифметическую прогресию.найти ее первый член и n если: d=3; an=23; Sn=85
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pentV
A_n=23; a_1 + (n-1)*d = 23; a_1+ (n-1)*3=23; a_1+3n-3=23; a_1 + 3n = 26
a_1=26-3n
S_n= [(a_1 + a_n)*n]/2
85=[(a_1+23)*n]/2
170=(26-3n+23)*n
170=26n-3n^2+23n
3n²-49n+170=0
D=(-49)^2-4*3*170=7^4-12*170=2401-2040=361=19²
n_1=(49+19)/6=68/6--нацело не делится, не подходит
n_2=(49-19)/6=5
a_1=26-3n
a_1=26-3*5=11
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Answers & Comments
a_1=26-3n
S_n= [(a_1 + a_n)*n]/2
85=[(a_1+23)*n]/2
170=(26-3n+23)*n
170=26n-3n^2+23n
3n²-49n+170=0
D=(-49)^2-4*3*170=7^4-12*170=2401-2040=361=19²
n_1=(49+19)/6=68/6--нацело не делится, не подходит
n_2=(49-19)/6=5
a_1=26-3n
a_1=26-3*5=11