Question

найдите сумму первых семи членов геометрической прогрессии
16;8;4;.........​

Answer 1

$b_{1}=16\\b_{2}=8\\b_{2}=b_{1}*q\\q=b_{2}:b_{1}=8:16=\frac{1}{2}\\\\S_{7}=\frac{b_{1}(1-q^{7})}{1-q}=\frac{16*(1-(\frac{1}{2})^{7})}{1-\frac{1}{2} }=16*2*(1-\frac{1}{128})=2^{5} *\frac{127}{2^{7} }= \frac{127}{4}=31,75$