সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=75$$ এবং সাধারণ অনুপাত: $$r=3.8$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {3.8}^{2-1}=75\cdot {3.8}^1=75\cdot 3.8=285$$

$$a_3=a_1·r^{n-1}=75\cdot {3.8}^{3-1}=75\cdot {3.8}^2=75\cdot 14.44=1083$$

$$a_4=a_1·r^{n-1}=75\cdot {3.8}^{4-1}=75\cdot {3.8}^3=75\cdot 54.87199999999999=4115.4$$

$$a_5=a_1·r^{n-1}=75\cdot {3.8}^{5-1}=75\cdot {3.8}^4=75\cdot 208.51359999999997=15638.519999999997$$

$$a_6=a_1·r^{n-1}=75\cdot {3.8}^{6-1}=75\cdot {3.8}^5=75\cdot 792.3516799999998=59426.37599999998$$

$$a_7=a_1·r^{n-1}=75\cdot {3.8}^{7-1}=75\cdot {3.8}^6=75\cdot 3010.936383999999=225820.22879999992$$

$$a_8=a_1·r^{n-1}=75\cdot {3.8}^{8-1}=75\cdot {3.8}^7=75\cdot 11441.558259199996=858116.8694399997$$

$$a_9=a_1·r^{n-1}=75\cdot {3.8}^{9-1}=75\cdot {3.8}^8=75\cdot 43477.921384959984=3260844.103871999$$

$$a_{10}=a_1·r^{n-1}=75\cdot {3.8}^{10-1}=75\cdot {3.8}^9=75\cdot 165216.10126284792=12391207.594713595$$