সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=275$$ এবং সাধারণ অনুপাত: $$r=1.1818181818181819$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=275$$

$$a_2=a_1·r^{n-1}=275\cdot {1.1818181818181819}^{2-1}=275\cdot {1.1818181818181819}^1=275\cdot 1.1818181818181819=325$$

$$a_3=a_1·r^{n-1}=275\cdot {1.1818181818181819}^{3-1}=275\cdot {1.1818181818181819}^2=275\cdot 1.3966942148760333=384.0909090909092$$

$$a_4=a_1·r^{n-1}=275\cdot {1.1818181818181819}^{4-1}=275\cdot {1.1818181818181819}^3=275\cdot 1.6506386175807666=453.9256198347108$$

$$a_5=a_1·r^{n-1}=275\cdot {1.1818181818181819}^{5-1}=275\cdot {1.1818181818181819}^4=275\cdot 1.9507547298681789=536.4575507137492$$

$$a_6=a_1·r^{n-1}=275\cdot {1.1818181818181819}^{6-1}=275\cdot {1.1818181818181819}^5=275\cdot 2.30543740802603=633.9952872071582$$

$$a_7=a_1·r^{n-1}=275\cdot {1.1818181818181819}^{7-1}=275\cdot {1.1818181818181819}^6=275\cdot 2.7246078458489444=749.2671576084597$$

$$a_8=a_1·r^{n-1}=275\cdot {1.1818181818181819}^{8-1}=275\cdot {1.1818181818181819}^7=275\cdot 3.2199910905487523=885.4975499009068$$

$$a_9=a_1·r^{n-1}=275\cdot {1.1818181818181819}^{9-1}=275\cdot {1.1818181818181819}^8=275\cdot 3.8054440161030714=1046.4971044283445$$

$$a_{10}=a_1·r^{n-1}=275\cdot {1.1818181818181819}^{10-1}=275\cdot {1.1818181818181819}^9=275\cdot 4.497342928121812=1236.7693052334982$$