解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=75$$ 和公比：$$r=2.56$$ 插入几何级数的公式：

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {2.56}^{2-1}=75\cdot {2.56}^1=75\cdot 2.56=192$$

$$a_3=a_1·r^{n-1}=75\cdot {2.56}^{3-1}=75\cdot {2.56}^2=75\cdot 6.5536=491.52000000000004$$

$$a_4=a_1·r^{n-1}=75\cdot {2.56}^{4-1}=75\cdot {2.56}^3=75\cdot 16.777216000000003=1258.2912000000001$$

$$a_5=a_1·r^{n-1}=75\cdot {2.56}^{5-1}=75\cdot {2.56}^4=75\cdot 42.94967296=3221.225472$$

$$a_6=a_1·r^{n-1}=75\cdot {2.56}^{6-1}=75\cdot {2.56}^5=75\cdot 109.95116277760002=8246.337208320001$$

$$a_7=a_1·r^{n-1}=75\cdot {2.56}^{7-1}=75\cdot {2.56}^6=75\cdot 281.47497671065605=21110.623253299203$$

$$a_8=a_1·r^{n-1}=75\cdot {2.56}^{8-1}=75\cdot {2.56}^7=75\cdot 720.5759403792795=54043.19552844596$$

$$a_9=a_1·r^{n-1}=75\cdot {2.56}^{9-1}=75\cdot {2.56}^8=75\cdot 1844.6744073709556=138350.58055282166$$

$$a_{10}=a_1·r^{n-1}=75\cdot {2.56}^{10-1}=75\cdot {2.56}^9=75\cdot 4722.3664828696465=354177.4862152235$$