সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=33$$ এবং সাধারণ অনুপাত: $$r=0.3939393939393939$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=33$$

$$a_2=a_1·r^{n-1}=33\cdot {0.3939393939393939}^{2-1}=33\cdot {0.3939393939393939}^1=33\cdot 0.3939393939393939=13$$

$$a_3=a_1·r^{n-1}=33\cdot {0.3939393939393939}^{3-1}=33\cdot {0.3939393939393939}^2=33\cdot 0.155188246097337=5.121212121212121$$

$$a_4=a_1·r^{n-1}=33\cdot {0.3939393939393939}^{4-1}=33\cdot {0.3939393939393939}^3=33\cdot 0.06113476361410245=2.017447199265381$$

$$a_5=a_1·r^{n-1}=33\cdot {0.3939393939393939}^{5-1}=33\cdot {0.3939393939393939}^4=33\cdot 0.02408339172676763=0.7947519269833319$$

$$a_6=a_1·r^{n-1}=33\cdot {0.3939393939393939}^{6-1}=33\cdot {0.3939393939393939}^5=33\cdot 0.009487396740847854=0.3130840924479792$$

$$a_7=a_1·r^{n-1}=33\cdot {0.3939393939393939}^{7-1}=33\cdot {0.3939393939393939}^6=33\cdot 0.003737459322152185=0.1233361576310221$$

$$a_8=a_1·r^{n-1}=33\cdot {0.3939393939393939}^{8-1}=33\cdot {0.3939393939393939}^7=33\cdot 0.0014723324602417696=0.048586971187978396$$

$$a_9=a_1·r^{n-1}=33\cdot {0.3939393939393939}^{9-1}=33\cdot {0.3939393939393939}^8=33\cdot 0.0005800097570649395=0.019140321983143003$$

$$a_{10}=a_1·r^{n-1}=33\cdot {0.3939393939393939}^{10-1}=33\cdot {0.3939393939393939}^9=33\cdot 0.00022848869217709738=0.0075401268418442136$$