解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=65$$ 和公比：$$r=26$$ 插入几何级数的公式：

$$a_1=65$$

$$a_2=a_1·r^{n-1}=65\cdot {26}^{2-1}=65\cdot {26}^1=65\cdot 26=1690$$

$$a_3=a_1·r^{n-1}=65\cdot {26}^{3-1}=65\cdot {26}^2=65\cdot 676=43940$$

$$a_4=a_1·r^{n-1}=65\cdot {26}^{4-1}=65\cdot {26}^3=65\cdot 17576=1142440$$

$$a_5=a_1·r^{n-1}=65\cdot {26}^{5-1}=65\cdot {26}^4=65\cdot 456976=29703440$$

$$a_6=a_1·r^{n-1}=65\cdot {26}^{6-1}=65\cdot {26}^5=65\cdot 11881376=772289440$$

$$a_7=a_1·r^{n-1}=65\cdot {26}^{7-1}=65\cdot {26}^6=65\cdot 308915776=20079525440$$

$$a_8=a_1·r^{n-1}=65\cdot {26}^{8-1}=65\cdot {26}^7=65\cdot 8031810176=522067661440$$

$$a_9=a_1·r^{n-1}=65\cdot {26}^{9-1}=65\cdot {26}^8=65\cdot 208827064576=13573759197440$$

$$a_{10}=a_1·r^{n-1}=65\cdot {26}^{10-1}=65\cdot {26}^9=65\cdot 5429503678976=352917739133440$$