解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=156$$ 和公比：$$r=1.3076923076923077$$ 插入几何级数的公式：

$$a_1=156$$

$$a_2=a_1·r^{n-1}=156\cdot {1.3076923076923077}^{2-1}=156\cdot {1.3076923076923077}^1=156\cdot 1.3076923076923077=204$$

$$a_3=a_1·r^{n-1}=156\cdot {1.3076923076923077}^{3-1}=156\cdot {1.3076923076923077}^2=156\cdot 1.7100591715976332=266.7692307692308$$

$$a_4=a_1·r^{n-1}=156\cdot {1.3076923076923077}^{4-1}=156\cdot {1.3076923076923077}^3=156\cdot 2.236231224396905=348.8520710059172$$

$$a_5=a_1·r^{n-1}=156\cdot {1.3076923076923077}^{5-1}=156\cdot {1.3076923076923077}^4=156\cdot 2.9243023703651834=456.1911697769686$$

$$a_6=a_1·r^{n-1}=156\cdot {1.3076923076923077}^{6-1}=156\cdot {1.3076923076923077}^5=156\cdot 3.8240877150929324=596.5576835544974$$

$$a_7=a_1·r^{n-1}=156\cdot {1.3076923076923077}^{7-1}=156\cdot {1.3076923076923077}^6=156\cdot 5.000730088967681=780.1138938789583$$

$$a_8=a_1·r^{n-1}=156\cdot {1.3076923076923077}^{8-1}=156\cdot {1.3076923076923077}^7=156\cdot 6.5394162701885055=1020.1489381494068$$

$$a_9=a_1·r^{n-1}=156\cdot {1.3076923076923077}^{9-1}=156\cdot {1.3076923076923077}^8=156\cdot 8.55154435332343=1334.0409191184551$$

$$a_{10}=a_1·r^{n-1}=156\cdot {1.3076923076923077}^{10-1}=156\cdot {1.3076923076923077}^9=156\cdot 11.18278876973064=1744.5150480779798$$