Question

b1=3/5, q=-0.5, sn=3/8 найти n и bn ответ должен быть n=4 и bn=3/40

Answer 1

$b_{1}=\frac{3}{5}\\\\q=-0,5\\\\S_{n}=\frac{3}{8}\\\\S_{n}=\frac{b_{1}*(q^{n}-1)}{q-1}\\\\\frac{3}{8}=\frac{\frac{3}{5}*((-0,5)^{n}-1)}{-0,5-1}\\\\0,375=\frac{0,6*((-0,5)^{n}-1) }{-1,5}\\\\0,375=-0,4*((-0,5)^{n}-1)\\\\(-0,5)^{n} -1=-0,9375\\\\(-0,5)^{n}=0,0625\\\\(-0,5)^{n}=(-0,5)^{4}\\\\n=4\\\\b_{4}=b_{1}*q^{3}=\frac{3}{5}*(-0,5)^{3}=\frac{3}{5}*(-\frac{1}{2})^{3} =\frac{3}{5}*(-\frac{1}{8})=-\frac{3}{40}$