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：$$r=0.7142857142857143$$ 插入几何级数的公式：

$$a_1=42$$

$$a_2=a_1·r^{n-1}=42\cdot {0.7142857142857143}^{2-1}=42\cdot {0.7142857142857143}^1=42\cdot 0.7142857142857143=30$$

$$a_3=a_1·r^{n-1}=42\cdot {0.7142857142857143}^{3-1}=42\cdot {0.7142857142857143}^2=42\cdot 0.5102040816326531=21.42857142857143$$

$$a_4=a_1·r^{n-1}=42\cdot {0.7142857142857143}^{4-1}=42\cdot {0.7142857142857143}^3=42\cdot 0.3644314868804665=15.306122448979593$$

$$a_5=a_1·r^{n-1}=42\cdot {0.7142857142857143}^{5-1}=42\cdot {0.7142857142857143}^4=42\cdot 0.2603082049146189=10.932944606413995$$

$$a_6=a_1·r^{n-1}=42\cdot {0.7142857142857143}^{6-1}=42\cdot {0.7142857142857143}^5=42\cdot 0.18593443208187066=7.809246147438568$$

$$a_7=a_1·r^{n-1}=42\cdot {0.7142857142857143}^{7-1}=42\cdot {0.7142857142857143}^6=42\cdot 0.13281030862990761=5.57803296245612$$

$$a_8=a_1·r^{n-1}=42\cdot {0.7142857142857143}^{8-1}=42\cdot {0.7142857142857143}^7=42\cdot 0.09486450616421974=3.984309258897229$$

$$a_9=a_1·r^{n-1}=42\cdot {0.7142857142857143}^{9-1}=42\cdot {0.7142857142857143}^8=42\cdot 0.06776036154587124=2.845935184926592$$

$$a_{10}=a_1·r^{n-1}=42\cdot {0.7142857142857143}^{10-1}=42\cdot {0.7142857142857143}^9=42\cdot 0.04840025824705089=2.032810846376137$$