解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=57$$ 和公比：$$r=0.7894736842105263$$ 插入几何级数的公式：

$$a_1=57$$

$$a_2=a_1·r^{n-1}=57\cdot {0.7894736842105263}^{2-1}=57\cdot {0.7894736842105263}^1=57\cdot 0.7894736842105263=45$$

$$a_3=a_1·r^{n-1}=57\cdot {0.7894736842105263}^{3-1}=57\cdot {0.7894736842105263}^2=57\cdot 0.6232686980609419=35.526315789473685$$

$$a_4=a_1·r^{n-1}=57\cdot {0.7894736842105263}^{4-1}=57\cdot {0.7894736842105263}^3=57\cdot 0.4920542353112699=28.047091412742386$$

$$a_5=a_1·r^{n-1}=57\cdot {0.7894736842105263}^{5-1}=57\cdot {0.7894736842105263}^4=57\cdot 0.3884638699825815=22.142440589007144$$

$$a_6=a_1·r^{n-1}=57\cdot {0.7894736842105263}^{6-1}=57\cdot {0.7894736842105263}^5=57\cdot 0.3066820026178275=17.48087414921617$$

$$a_7=a_1·r^{n-1}=57\cdot {0.7894736842105263}^{7-1}=57\cdot {0.7894736842105263}^6=57\cdot 0.24211737048775855=13.800690117802237$$

$$a_8=a_1·r^{n-1}=57\cdot {0.7894736842105263}^{8-1}=57\cdot {0.7894736842105263}^7=57\cdot 0.1911452924903357=10.895281671949135$$

$$a_9=a_1·r^{n-1}=57\cdot {0.7894736842105263}^{9-1}=57\cdot {0.7894736842105263}^8=57\cdot 0.150904178281844=8.601538162065108$$

$$a_{10}=a_1·r^{n-1}=57\cdot {0.7894736842105263}^{10-1}=57\cdot {0.7894736842105263}^9=57\cdot 0.11913487759092946=6.790688022682979$$