Question

5. Найдите разность арифметической прогрессии и n, если a1=3 и an=11, S=28​

Answer 1

Ответ: n=4,   d=8/3.

Объяснение:

$\displaystyle\\a_1=3\ \ \ \ \ \ a_n=11\ \ \ \ \ \ S_n=28\ \ \ \ \ \ d=?\ \ \ \ \ \ n=?\\\\\left \{ {{a_n=a_1+(n-1)*d} \atop {S_n=\frac{a_1+a_n}{2}}*n \right. \ \ \ \ \ \ \left \{ {{3+(n-1)*d=11} \atop {\frac{3+11}{2}*n=28 }} \right.\ \ \ \ \ \ \left \{ {{(n-1)*d=8} \atop {7n=28\ |:7}} \right. \\\\\\\left \{ {{(4-1)*d=8} \atop {n=4}} \right. \ \ \ \ \ \ \left \{ {{3*d=8\ |:3} \atop {n=4}} \right. \ \ \ \ \ \ \left \{ {{d=\frac{8}{3}=2\frac{2}{3} } \atop {n=4}} \right. .$