解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=64$$ 和公比：$$r=1.6875$$ 插入几何级数的公式：

$$a_1=64$$

$$a_2=a_1·r^{n-1}=64\cdot {1.6875}^{2-1}=64\cdot {1.6875}^1=64\cdot 1.6875=108$$

$$a_3=a_1·r^{n-1}=64\cdot {1.6875}^{3-1}=64\cdot {1.6875}^2=64\cdot 2.84765625=182.25$$

$$a_4=a_1·r^{n-1}=64\cdot {1.6875}^{4-1}=64\cdot {1.6875}^3=64\cdot 4.805419921875=307.546875$$

$$a_5=a_1·r^{n-1}=64\cdot {1.6875}^{5-1}=64\cdot {1.6875}^4=64\cdot 8.109146118164062=518.9853515625$$

$$a_6=a_1·r^{n-1}=64\cdot {1.6875}^{6-1}=64\cdot {1.6875}^5=64\cdot 13.684184074401855=875.7877807617188$$

$$a_7=a_1·r^{n-1}=64\cdot {1.6875}^{7-1}=64\cdot {1.6875}^6=64\cdot 23.09206062555313=1477.8918800354004$$

$$a_8=a_1·r^{n-1}=64\cdot {1.6875}^{8-1}=64\cdot {1.6875}^7=64\cdot 38.96785230562091=2493.942547559738$$

$$a_9=a_1·r^{n-1}=64\cdot {1.6875}^{9-1}=64\cdot {1.6875}^8=64\cdot 65.75825076573528=4208.528049007058$$

$$a_{10}=a_1·r^{n-1}=64\cdot {1.6875}^{10-1}=64\cdot {1.6875}^9=64\cdot 110.96704816717829=7101.891082699411$$