解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=42$$ 和公比：$$r=2.0476190476190474$$ 插入几何级数的公式：

$$a_1=42$$

$$a_2=a_1·r^{n-1}=42\cdot {2.0476190476190474}^{2-1}=42\cdot {2.0476190476190474}^1=42\cdot 2.0476190476190474=86$$

$$a_3=a_1·r^{n-1}=42\cdot {2.0476190476190474}^{3-1}=42\cdot {2.0476190476190474}^2=42\cdot 4.192743764172335=176.09523809523807$$

$$a_4=a_1·r^{n-1}=42\cdot {2.0476190476190474}^{4-1}=42\cdot {2.0476190476190474}^3=42\cdot 8.585141993305257=360.5759637188208$$

$$a_5=a_1·r^{n-1}=42\cdot {2.0476190476190474}^{5-1}=42\cdot {2.0476190476190474}^4=42\cdot 17.579100272006=738.3222114242519$$

$$a_6=a_1·r^{n-1}=42\cdot {2.0476190476190474}^{6-1}=42\cdot {2.0476190476190474}^5=42\cdot 35.995300556964665=1511.802623392516$$

$$a_7=a_1·r^{n-1}=42\cdot {2.0476190476190474}^{7-1}=42\cdot {2.0476190476190474}^6=42\cdot 73.70466304521335=3095.5958478989605$$

$$a_8=a_1·r^{n-1}=42\cdot {2.0476190476190474}^{8-1}=42\cdot {2.0476190476190474}^7=42\cdot 150.91907194972256=6338.6010218883475$$

$$a_9=a_1·r^{n-1}=42\cdot {2.0476190476190474}^{9-1}=42\cdot {2.0476190476190474}^8=42\cdot 309.02476637324145=12979.04018767614$$

$$a_{10}=a_1·r^{n-1}=42\cdot {2.0476190476190474}^{10-1}=42\cdot {2.0476190476190474}^9=42\cdot 632.7649978118752=26576.12990809876$$