Question

Помогите по алгебре!

Answer 1

$\displaystyle\bf\\1) \ \ a_{5} =11 \ \ ; \ \ a_{8} =17\\\\\\-\left \{ {{a_{1} +7d=17} \atop {a_{1}+4d=11 }} \right. \\---------\\3d=6\\\\d=2\\\\a_{1} =11-4d=11-4\cdot2=11-8=3\\\\\boxed{a_{1} =3}\\\\a_{10} =a_{1} +9d=3+9\cdot 2=3+18=21\\\\\\S_{10} =\frac{a_{1} +a_{10} }{2} \cdot10=(a_{1} +a_{10} )\cdot 5=(3+21)\cdot 5=24\cdot5=120\\\\\\\boxed{S_{10} =120}$

$\displaystyle\bf\\2) \ \ b_{n} =\frac{3}{4^{n} } \\\\\\b_{1} =\frac{3}{4^{1} } =\frac{3}{4} \\\\\\b_{2} =\frac{3}{4^{2} } =\frac{3}{16} \\\\\\b_{2} =b_{1} \cdot q\\\\\\q=b_{2} :b_{1} =\frac{3}{16} :\frac{3}{4} =\frac{3}{16} \cdot\frac{4}{3} =\frac{1}{4} \\\\\\\boxed{q=\frac{1}{4} }\\\\\\S=\frac{b_{1} }{1-q} =\frac{\frac{3}{4} }{1-\frac{1}{4} } =\frac{\frac{3}{4} }{\frac{3}{4} } =1\\\\\\\boxed{S=1}$