Question

Определите число членов геометрической прогрессии, если
b1 = 81,
bn = 1/81
q = 1/3

Answer 1

$\displaystyle\bf\\b_{1} =81\\\\b_{n} =\frac{1}{81} \\\\q=\frac{1}{3} \\\\n=?\\\\\\b_{n} =b_{1} \cdot q^{n-1} \\\\\\\frac{1}{81} =81\cdot\Big(\frac{1}{3} \Big)^{n-1} \\\\\\\Big(\frac{1}{3} \Big)^{n-1} =\frac{1}{81} :81\\\\\\\Big(\frac{1}{3} \Big)^{n-1} =\frac{1}{81^{2} } \\\\\\\Big(\frac{1}{3} \Big)^{n-1} =\Big(\frac{1}{3} \Big)^{8} \\\\\\n-1=8\\\\\boxed{n=9}$