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解答 - 几何数列

公比是：

r = 0.042105263157894736

r=0.042105263157894736

该系列的和是：

s = 98

s=98

此系列的通用形式是：

a_{n} = 95 \cdot {0.042105263157894736}^{n - 1}

a_n=95*0.042105263157894736^(n-1)

这个序列的第n项是：

95, 4, 0.16842105263157894, 0.007091412742382271, 0.0002985857996792535, 1.257203367070541 E - 05, 5.293487861349646 E - 07, 2.2288369942524824 E - 08, 9.38457681790519 E - 10, 3.951400765433764 E - 11

95,4,0.16842105263157894,0.007091412742382271,0.0002985857996792535,1.257203367070541E-05,5.293487861349646E-07,2.2288369942524824E-08,9.38457681790519E-10,3.951400765433764E-11

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：

$a_{2} a_{1} = \frac{4}{95} = 0.042105263157894736$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.042105263157894736$

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： $a = 95$ 、公比： $r = 0.042105263157894736$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 95 * ((1 - {0.042105263157894736}^{2}) / (1 - 0.042105263157894736))$

$s_{2} = 95 * ((1 - 0.0017728531855955678) / (1 - 0.042105263157894736))$

$s_{2} = 95 * (0.9982271468144044 / (1 - 0.042105263157894736))$

$s_{2} = 95 * (0.9982271468144044 / 0.9578947368421052)$

$s_{2} = 95 \cdot 1.0421052631578946$

$s_{2} = 98.99999999999999$

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： $a = 95$ 和公比： $r = 0.042105263157894736$ 插入几何级数的公式：

$a_{n} = 95 \cdot {0.042105263157894736}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 95$

$a_{2} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.042105263157894736}^{2 - 1} = 95 \cdot {0.042105263157894736}^{1} = 95 \cdot 0.042105263157894736 = 4$

$a_{3} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.042105263157894736}^{3 - 1} = 95 \cdot {0.042105263157894736}^{2} = 95 \cdot 0.0017728531855955678 = 0.16842105263157894$

$a_{4} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.042105263157894736}^{4 - 1} = 95 \cdot {0.042105263157894736}^{3} = 95 \cdot 7.464644991981338 E - 05 = 0.007091412742382271$

$a_{5} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.042105263157894736}^{5 - 1} = 95 \cdot {0.042105263157894736}^{4} = 95 \cdot 3.1430084176763526 E - 06 = 0.0002985857996792535$

$a_{6} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.042105263157894736}^{6 - 1} = 95 \cdot {0.042105263157894736}^{5} = 95 \cdot 1.3233719653374116 E - 07 = 1.257203367070541 E - 05$

$a_{7} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.042105263157894736}^{7 - 1} = 95 \cdot {0.042105263157894736}^{6} = 95 \cdot 5.572092485631207 E - 09 = 5.293487861349646 E - 07$

$a_{8} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.042105263157894736}^{8 - 1} = 95 \cdot {0.042105263157894736}^{7} = 95 \cdot 2.3461442044762974 E - 10 = 2.2288369942524824 E - 08$

$a_{9} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.042105263157894736}^{9 - 1} = 95 \cdot {0.042105263157894736}^{8} = 95 \cdot 9.878501913584411 E - 12 = 9.38457681790519 E - 10$

$a_{10} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.042105263157894736}^{10 - 1} = 95 \cdot {0.042105263157894736}^{9} = 95 \cdot 4.159369226772383 E - 13 = 3.951400765433764 E - 11$

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