Question

A7+a4=6
a5-a2=12
Найти: a1,d

Answer 1

ответ: a₁=195/20

a₃=$9\frac{9}{10}$

Объяснение:

aₙ=a₁+d(n-1)

a₇=a₁+d(7-1)=a₁+6d

a₄=a₁+d(4-1)=a₁+3d

a₅=a₁+d(5-1)=a₁+4d

a2=a₁+d(2-1)=

Составим систему

$\left \{ {{a1+6d+a1+3d=6} \atop {a1+4d+a1+d=12}} \right. \\\left \{ {{2a1+9d=6} \atop {2a1+5d=12}} \right. \\\left \{ {{2a1=6-9d} \atop {6-9d+5d=12}} \right. \\\left \{ {{2a1=6-9d} \atop {-4d=12-6}} \right. \\\left \{ {{2a1=6-9d} \atop {d=-6/4}} \right. \\\left \{ {{2a1=6-9(-1,5)} \atop {d=-1,5}} \right. \\\left \{ {{2a1=6+13,5} \atop {d=-1,5}} \right. \\\left \{ {{a1=19,5/2} \atop {d=-1,5}} \right. \\\left \{ {{a1=195/20} \atop {d=-1,5}} \right.$

a₁=195/20

a₃=a₁+2d=$\frac{195-2(-1,5)}{20} =\frac{195+3}{20} =\frac{198}{20} =9\frac{18}{20} =9\frac{9}{10}$