解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=57$$ 和公比：$$r=1.1578947368421053$$ 插入几何级数的公式：

$$a_1=57$$

$$a_2=a_1·r^{n-1}=57\cdot {1.1578947368421053}^{2-1}=57\cdot {1.1578947368421053}^1=57\cdot 1.1578947368421053=66$$

$$a_3=a_1·r^{n-1}=57\cdot {1.1578947368421053}^{3-1}=57\cdot {1.1578947368421053}^2=57\cdot 1.3407202216066483=76.42105263157895$$

$$a_4=a_1·r^{n-1}=57\cdot {1.1578947368421053}^{4-1}=57\cdot {1.1578947368421053}^3=57\cdot 1.5524128881761192=88.4875346260388$$

$$a_5=a_1·r^{n-1}=57\cdot {1.1578947368421053}^{5-1}=57\cdot {1.1578947368421053}^4=57\cdot 1.7975307126249802=102.45925061962387$$

$$a_6=a_1·r^{n-1}=57\cdot {1.1578947368421053}^{6-1}=57\cdot {1.1578947368421053}^5=57\cdot 2.0813513514605035=118.6370270332487$$

$$a_7=a_1·r^{n-1}=57\cdot {1.1578947368421053}^{7-1}=57\cdot {1.1578947368421053}^6=57\cdot 2.4099857753753198=137.36918919639322$$

$$a_8=a_1·r^{n-1}=57\cdot {1.1578947368421053}^{8-1}=57\cdot {1.1578947368421053}^7=57\cdot 2.790509845171423=159.05906117477113$$

$$a_9=a_1·r^{n-1}=57\cdot {1.1578947368421053}^{9-1}=57\cdot {1.1578947368421053}^8=57\cdot 3.231116662830069=184.17364978131394$$

$$a_{10}=a_1·r^{n-1}=57\cdot {1.1578947368421053}^{10-1}=57\cdot {1.1578947368421053}^9=57\cdot 3.7412929780137643=213.25369974678458$$