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解答 - 几何数列

公比是：

r = 0.0009971509971509972

r=0.0009971509971509972

该系列的和是：

s = 35135

s=35135

此系列的通用形式是：

a_{n} = 35100 \cdot {0.0009971509971509972}^{n - 1}

a_n=35100*0.0009971509971509972^(n-1)

这个序列的第n项是：

35100, 35, 0.034900284900284906, 3.4800853889172984 E - 05, 3.4701706157295005 E - 08, 3.460284089758761 E - 11, 3.45042573052868 E - 14, 3.4405954577921306 E - 17, 3.4307931915306144 E - 20, 3.421018851953605 E - 23

35100,35,0.034900284900284906,3.4800853889172984E-05,3.4701706157295005E-08,3.460284089758761E-11,3.45042573052868E-14,3.4405954577921306E-17,3.4307931915306144E-20,3.421018851953605E-23

查看步骤

逐步解答

1. 找到公比

通过将序列中的任何项除以前一项来找到公比：

$a_{2} a_{1} = \frac{35}{35100} = 0.0009971509971509972$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.0009971509971509972$

2. 求和

5 个额外步骤

$s_{n} = a * ((1 - r^{n}) / (1 - r))$

要找到系列的和，将第一项： $a = 35, 100$ 、公比： $r = 0.0009971509971509972$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 35100 * ((1 - {0.0009971509971509972}^{2}) / (1 - 0.0009971509971509972))$

$s_{2} = 35100 * ((1 - 9.94310111119228 E - 07) / (1 - 0.0009971509971509972))$

$s_{2} = 35100 * (0.9999990056898889 / (1 - 0.0009971509971509972))$

$s_{2} = 35100 * (0.9999990056898889 / 0.999002849002849)$

$s_{2} = 35100 \cdot 1.000997150997151$

$s_{2} = 35135$

3. 找到通用形式

$a_{n} = a \cdot r^{n - 1}$

要找到系列的通用形式，将第一项： $a = 35, 100$ 和公比： $r = 0.0009971509971509972$ 插入几何级数的公式：

$a_{n} = 35100 \cdot {0.0009971509971509972}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 35100$

$a_{2} = a_{1} \cdot r^{n - 1} = 35100 \cdot {0.0009971509971509972}^{2 - 1} = 35100 \cdot {0.0009971509971509972}^{1} = 35100 \cdot 0.0009971509971509972 = 35$

$a_{3} = a_{1} \cdot r^{n - 1} = 35100 \cdot {0.0009971509971509972}^{3 - 1} = 35100 \cdot {0.0009971509971509972}^{2} = 35100 \cdot 9.94310111119228 E - 07 = 0.034900284900284906$

$a_{4} = a_{1} \cdot r^{n - 1} = 35100 \cdot {0.0009971509971509972}^{4 - 1} = 35100 \cdot {0.0009971509971509972}^{3} = 35100 \cdot 9.914773187798571 E - 10 = 3.4800853889172984 E - 05$

$a_{5} = a_{1} \cdot r^{n - 1} = 35100 \cdot {0.0009971509971509972}^{5 - 1} = 35100 \cdot {0.0009971509971509972}^{4} = 35100 \cdot 9.886525970739317 E - 13 = 3.4701706157295005 E - 08$

$a_{6} = a_{1} \cdot r^{n - 1} = 35100 \cdot {0.0009971509971509972}^{6 - 1} = 35100 \cdot {0.0009971509971509972}^{5} = 35100 \cdot 9.85835923008194 E - 16 = 3.460284089758761 E - 11$

$a_{7} = a_{1} \cdot r^{n - 1} = 35100 \cdot {0.0009971509971509972}^{7 - 1} = 35100 \cdot {0.0009971509971509972}^{6} = 35100 \cdot 9.830272736548945 E - 19 = 3.45042573052868 E - 14$

$a_{8} = a_{1} \cdot r^{n - 1} = 35100 \cdot {0.0009971509971509972}^{8 - 1} = 35100 \cdot {0.0009971509971509972}^{7} = 35100 \cdot 9.802266261516041 E - 22 = 3.4405954577921306 E - 17$

$a_{9} = a_{1} \cdot r^{n - 1} = 35100 \cdot {0.0009971509971509972}^{9 - 1} = 35100 \cdot {0.0009971509971509972}^{8} = 35100 \cdot 9.774339577010298 E - 25 = 3.4307931915306144 E - 20$

$a_{10} = a_{1} \cdot r^{n - 1} = 35100 \cdot {0.0009971509971509972}^{10 - 1} = 35100 \cdot {0.0009971509971509972}^{9} = 35100 \cdot 9.746492455708276 E - 28 = 3.421018851953605 E - 23$

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几何数列