解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=10$$ 和公比：$$r=1.6$$ 插入几何级数的公式：

$$a_1=10$$

$$a_2=a_1·r^{n-1}=10\cdot {1.6}^{2-1}=10\cdot {1.6}^1=10\cdot 1.6=16$$

$$a_3=a_1·r^{n-1}=10\cdot {1.6}^{3-1}=10\cdot {1.6}^2=10\cdot 2.5600000000000005=25.600000000000005$$

$$a_4=a_1·r^{n-1}=10\cdot {1.6}^{4-1}=10\cdot {1.6}^3=10\cdot 4.096000000000001=40.96000000000001$$

$$a_5=a_1·r^{n-1}=10\cdot {1.6}^{5-1}=10\cdot {1.6}^4=10\cdot 6.553600000000001=65.53600000000002$$

$$a_6=a_1·r^{n-1}=10\cdot {1.6}^{6-1}=10\cdot {1.6}^5=10\cdot 10.485760000000003=104.85760000000002$$

$$a_7=a_1·r^{n-1}=10\cdot {1.6}^{7-1}=10\cdot {1.6}^6=10\cdot 16.777216000000006=167.77216000000007$$

$$a_8=a_1·r^{n-1}=10\cdot {1.6}^{8-1}=10\cdot {1.6}^7=10\cdot 26.84354560000001=268.4354560000001$$

$$a_9=a_1·r^{n-1}=10\cdot {1.6}^{9-1}=10\cdot {1.6}^8=10\cdot 42.94967296000002=429.4967296000002$$

$$a_{10}=a_1·r^{n-1}=10\cdot {1.6}^{10-1}=10\cdot {1.6}^9=10\cdot 68.71947673600003=687.1947673600004$$