解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=100$$ 和公比：$$r=0.78$$ 插入几何级数的公式：

$$a_1=100$$

$$a_2=a_1·r^{n-1}=100\cdot {0.78}^{2-1}=100\cdot {0.78}^1=100\cdot 0.78=78$$

$$a_3=a_1·r^{n-1}=100\cdot {0.78}^{3-1}=100\cdot {0.78}^2=100\cdot 0.6084=60.84$$

$$a_4=a_1·r^{n-1}=100\cdot {0.78}^{4-1}=100\cdot {0.78}^3=100\cdot 0.47455200000000003=47.455200000000005$$

$$a_5=a_1·r^{n-1}=100\cdot {0.78}^{5-1}=100\cdot {0.78}^4=100\cdot 0.3701505600000001=37.01505600000001$$

$$a_6=a_1·r^{n-1}=100\cdot {0.78}^{6-1}=100\cdot {0.78}^5=100\cdot 0.28871743680000006=28.871743680000005$$

$$a_7=a_1·r^{n-1}=100\cdot {0.78}^{7-1}=100\cdot {0.78}^6=100\cdot 0.22519960070400005=22.519960070400007$$

$$a_8=a_1·r^{n-1}=100\cdot {0.78}^{8-1}=100\cdot {0.78}^7=100\cdot 0.17565568854912003=17.565568854912$$

$$a_9=a_1·r^{n-1}=100\cdot {0.78}^{9-1}=100\cdot {0.78}^8=100\cdot 0.13701143706831365=13.701143706831365$$

$$a_{10}=a_1·r^{n-1}=100\cdot {0.78}^{10-1}=100\cdot {0.78}^9=100\cdot 0.10686892091328463=10.686892091328463$$