解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=56$$ 和公比：$$r=1.6607142857142858$$ 插入几何级数的公式：

$$a_1=56$$

$$a_2=a_1·r^{n-1}=56\cdot {1.6607142857142858}^{2-1}=56\cdot {1.6607142857142858}^1=56\cdot 1.6607142857142858=93$$

$$a_3=a_1·r^{n-1}=56\cdot {1.6607142857142858}^{3-1}=56\cdot {1.6607142857142858}^2=56\cdot 2.7579719387755106=154.44642857142858$$

$$a_4=a_1·r^{n-1}=56\cdot {1.6607142857142858}^{4-1}=56\cdot {1.6607142857142858}^3=56\cdot 4.580203398323616=256.49139030612247$$

$$a_5=a_1·r^{n-1}=56\cdot {1.6607142857142858}^{5-1}=56\cdot {1.6607142857142858}^4=56\cdot 7.606409215073148=425.95891604409627$$

$$a_6=a_1·r^{n-1}=56\cdot {1.6607142857142858}^{6-1}=56\cdot {1.6607142857142858}^5=56\cdot 12.632072446460764=707.3960570018028$$

$$a_7=a_1·r^{n-1}=56\cdot {1.6607142857142858}^{7-1}=56\cdot {1.6607142857142858}^6=56\cdot 20.9782631700152=1174.7827375208512$$

$$a_8=a_1·r^{n-1}=56\cdot {1.6607142857142858}^{8-1}=56\cdot {1.6607142857142858}^7=56\cdot 34.8389013359181=1950.9784748114137$$

$$a_9=a_1·r^{n-1}=56\cdot {1.6607142857142858}^{9-1}=56\cdot {1.6607142857142858}^8=56\cdot 57.85746114714971=3240.0178242403836$$

$$a_{10}=a_1·r^{n-1}=56\cdot {1.6607142857142858}^{10-1}=56\cdot {1.6607142857142858}^9=56\cdot 96.08471226223077=5380.7438866849225$$