输入一个方程或问题

无法识别摄像头输入！

解答 - 几何数列

公比是：

r = 3.3263157894736843

r=3.3263157894736843

该系列的和是：

s = 410

s=410

此系列的通用形式是：

a_{n} = 95 \cdot {3.3263157894736843}^{n - 1}

a_n=95*3.3263157894736843^(n-1)

这个序列的第n项是：

95, 316, 1051.1157894736841, 3496.343047091413, 11629.9410829567, 38684.85665488755, 128678.04950467861, 428023.8278260889, 1423742.416768885, 4735816.881041765

95,316,1051.1157894736841,3496.343047091413,11629.9410829567,38684.85665488755,128678.04950467861,428023.8278260889,1423742.416768885,4735816.881041765

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：

$a_{2} a_{1} = \frac{316}{95} = 3.3263157894736843$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 3.3263157894736843$

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： $r = 3.3263157894736843$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 95 * ((1 - {3.3263157894736843}^{2}) / (1 - 3.3263157894736843))$

$s_{2} = 95 * ((1 - 11.06437673130194) / (1 - 3.3263157894736843))$

$s_{2} = 95 * (- 10.06437673130194 / (1 - 3.3263157894736843))$

$s_{2} = 95 * (- 10.06437673130194 / - 2.3263157894736843)$

$s_{2} = 95 \cdot 4.326315789473684$

$s_{2} = 410.99999999999994$

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： $r = 3.3263157894736843$ 插入几何级数的公式：

$a_{n} = 95 \cdot {3.3263157894736843}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 95$

$a_{2} = a_{1} \cdot r^{n - 1} = 95 \cdot {3.3263157894736843}^{2 - 1} = 95 \cdot {3.3263157894736843}^{1} = 95 \cdot 3.3263157894736843 = 316$

$a_{3} = a_{1} \cdot r^{n - 1} = 95 \cdot {3.3263157894736843}^{3 - 1} = 95 \cdot {3.3263157894736843}^{2} = 95 \cdot 11.06437673130194 = 1051.1157894736841$

$a_{4} = a_{1} \cdot r^{n - 1} = 95 \cdot {3.3263157894736843}^{4 - 1} = 95 \cdot {3.3263157894736843}^{3} = 95 \cdot 36.80361102201488 = 3496.343047091413$

$a_{5} = a_{1} \cdot r^{n - 1} = 95 \cdot {3.3263157894736843}^{5 - 1} = 95 \cdot {3.3263157894736843}^{4} = 95 \cdot 122.4204324521758 = 11629.9410829567$

$a_{6} = a_{1} \cdot r^{n - 1} = 95 \cdot {3.3263157894736843}^{6 - 1} = 95 \cdot {3.3263157894736843}^{5} = 95 \cdot 407.209017419869 = 38684.85665488755$

$a_{7} = a_{1} \cdot r^{n - 1} = 95 \cdot {3.3263157894736843}^{7 - 1} = 95 \cdot {3.3263157894736843}^{6} = 95 \cdot 1354.5057842597748 = 128678.04950467861$

$a_{8} = a_{1} \cdot r^{n - 1} = 95 \cdot {3.3263157894736843}^{8 - 1} = 95 \cdot {3.3263157894736843}^{7} = 95 \cdot 4505.513977116725 = 428023.8278260889$

$a_{9} = a_{1} \cdot r^{n - 1} = 95 \cdot {3.3263157894736843}^{9 - 1} = 95 \cdot {3.3263157894736843}^{8} = 95 \cdot 14986.762281777737 = 1423742.416768885$

$a_{10} = a_{1} \cdot r^{n - 1} = 95 \cdot {3.3263157894736843}^{10 - 1} = 95 \cdot {3.3263157894736843}^{9} = 95 \cdot 49850.70401096595 = 4735816.881041765$

我们做得怎么样？

给我们反馈

为什么学习这个

几何序列常用于解释数学、物理、工程、生物、经济、计算机科学、金融等领域的概念，因此它们是我们工具箱中非常有用的工具。例如，几何序列最常见的应用之一就是计算已经获得或未付的复利，这是与金融相关的最常见活动之一，可能意味着赚取或失去大量的金钱！其他应用包括但不仅限于计算概率、测算随时间变化的放射性以及设计建筑物。

术语和主题

几何数列