Question

Найдите a1 и n, если: d=-7, an=-18, Sn=-20 (9класс)

Answer 1

Ответ: a₁=10   n=5.

Объяснение:

$\displaystyle\\d=-7\ \ \ \ a_n=-18\ \ \ \ S_n=-20\ \ \ \ a_1=?\ \ \ \ n=?\\\\\left \{ {{a_n=a_1+(n-1)*d} \atop {S_n=\frac{2a_1+(n-1)*d}{2} }*n} \right. \ \ \ \ \ \ \left \{ {{a_1+(n-1)*d=-18} \atop {\frac{a_1+a_1+(n-1)*d}{2} }*n=-20} \right.$

$\displaystyle\left \{ {{a_1+(n-1)*(-7)=-18} \atop {\frac{a_1-18}{2} *n=-20\ |*2}} \right. \ \ \ \ \ \ \left \{ {{a_1-7n+7=-18} \atop {(a_1-18)*n=-40}} \right. \\\\\\\left \{ {{a_1=7n-25} \atop {(7n-25-18)*n=-40}} \right. \ \ \ \ \ \ \left \{ {{a_1=7n-25} \atop {7n^2-43n+40=0}} \right.\\\\\\\ \left \{ {{a_1=7n-25} \atop {7n^2-35n-8n+40=0}} \right. \ \ \ \ \ \ \left \{ {{a_1=7n-25} \atop {7n*(n-5)-8*(n-5)=0}} \right.$

$\displaystyle\left \{ {{a_1=7n-25} \atop {(n-5)*(7n-8)=0}} \right. \ \ \ \ \ \ \left \{ {{a_1=7*5-25} \atop {n_5=5\in\ \ \ \ n_2=\frac{8}{7} \notin}} \right. .\ \ \ \ \ \ \left \{ {{a_1=10} \atop {n=5}} .\right.$