সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=55$$ এবং সাধারণ অনুপাত: $$r=1.9090909090909092$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=55$$

$$a_2=a_1·r^{n-1}=55\cdot {1.9090909090909092}^{2-1}=55\cdot {1.9090909090909092}^1=55\cdot 1.9090909090909092=105$$

$$a_3=a_1·r^{n-1}=55\cdot {1.9090909090909092}^{3-1}=55\cdot {1.9090909090909092}^2=55\cdot 3.6446280991735542=200.4545454545455$$

$$a_4=a_1·r^{n-1}=55\cdot {1.9090909090909092}^{4-1}=55\cdot {1.9090909090909092}^3=55\cdot 6.9579263711495125=382.68595041322317$$

$$a_5=a_1·r^{n-1}=55\cdot {1.9090909090909092}^{5-1}=55\cdot {1.9090909090909092}^4=55\cdot 13.283313981285433=730.5822689706988$$

$$a_6=a_1·r^{n-1}=55\cdot {1.9090909090909092}^{6-1}=55\cdot {1.9090909090909092}^5=55\cdot 25.359053964272192=1394.7479680349707$$

$$a_7=a_1·r^{n-1}=55\cdot {1.9090909090909092}^{7-1}=55\cdot {1.9090909090909092}^6=55\cdot 48.412739386337826=2662.7006662485805$$

$$a_8=a_1·r^{n-1}=55\cdot {1.9090909090909092}^{8-1}=55\cdot {1.9090909090909092}^7=55\cdot 92.42432064664494=5083.337635565472$$

$$a_9=a_1·r^{n-1}=55\cdot {1.9090909090909092}^{9-1}=55\cdot {1.9090909090909092}^8=55\cdot 176.44643032541308=9704.553667897719$$

$$a_{10}=a_1·r^{n-1}=55\cdot {1.9090909090909092}^{10-1}=55\cdot {1.9090909090909092}^9=55\cdot 336.8522760757886=18526.875184168373$$