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：$$r=1.4736842105263157$$ 插入几何级数的公式：

$$a_1=57$$

$$a_2=a_1·r^{n-1}=57\cdot {1.4736842105263157}^{2-1}=57\cdot {1.4736842105263157}^1=57\cdot 1.4736842105263157=84$$

$$a_3=a_1·r^{n-1}=57\cdot {1.4736842105263157}^{3-1}=57\cdot {1.4736842105263157}^2=57\cdot 2.1717451523545703=123.7894736842105$$

$$a_4=a_1·r^{n-1}=57\cdot {1.4736842105263157}^{4-1}=57\cdot {1.4736842105263157}^3=57\cdot 3.2004665403119983=182.4265927977839$$

$$a_5=a_1·r^{n-1}=57\cdot {1.4736842105263157}^{5-1}=57\cdot {1.4736842105263157}^4=57\cdot 4.716477006775576=268.8391893862078$$

$$a_6=a_1·r^{n-1}=57\cdot {1.4736842105263157}^{6-1}=57\cdot {1.4736842105263157}^5=57\cdot 6.950597694195586=396.1840685691484$$

$$a_7=a_1·r^{n-1}=57\cdot {1.4736842105263157}^{7-1}=57\cdot {1.4736842105263157}^6=57\cdot 10.242986075656653=583.8502063124292$$

$$a_8=a_1·r^{n-1}=57\cdot {1.4736842105263157}^{8-1}=57\cdot {1.4736842105263157}^7=57\cdot 15.094926848336117=860.4108303551586$$

$$a_9=a_1·r^{n-1}=57\cdot {1.4736842105263157}^{9-1}=57\cdot {1.4736842105263157}^8=57\cdot 22.245155355442698=1267.9738552602337$$

$$a_{10}=a_1·r^{n-1}=57\cdot {1.4736842105263157}^{10-1}=57\cdot {1.4736842105263157}^9=57\cdot 32.78233420802081=1868.5930498571863$$