সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=99$$ এবং সাধারণ অনুপাত: $$r=0.36363636363636365$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=99$$

$$a_2=a_1·r^{n-1}=99\cdot {0.36363636363636365}^{2-1}=99\cdot {0.36363636363636365}^1=99\cdot 0.36363636363636365=36$$

$$a_3=a_1·r^{n-1}=99\cdot {0.36363636363636365}^{3-1}=99\cdot {0.36363636363636365}^2=99\cdot 0.1322314049586777=13.090909090909092$$

$$a_4=a_1·r^{n-1}=99\cdot {0.36363636363636365}^{4-1}=99\cdot {0.36363636363636365}^3=99\cdot 0.04808414725770098=4.760330578512397$$

$$a_5=a_1·r^{n-1}=99\cdot {0.36363636363636365}^{5-1}=99\cdot {0.36363636363636365}^4=99\cdot 0.01748514445734581=1.7310293012772353$$

$$a_6=a_1·r^{n-1}=99\cdot {0.36363636363636365}^{6-1}=99\cdot {0.36363636363636365}^5=99\cdot 0.0063582343481257495=0.6294652004644492$$

$$a_7=a_1·r^{n-1}=99\cdot {0.36363636363636365}^{7-1}=99\cdot {0.36363636363636365}^6=99\cdot 0.0023120852175002727=0.228896436532527$$

$$a_8=a_1·r^{n-1}=99\cdot {0.36363636363636365}^{8-1}=99\cdot {0.36363636363636365}^7=99\cdot 0.0008407582609091901=0.08323506783000982$$

$$a_9=a_1·r^{n-1}=99\cdot {0.36363636363636365}^{9-1}=99\cdot {0.36363636363636365}^8=99\cdot 0.00030573027669425094=0.030267297392730843$$

$$a_{10}=a_1·r^{n-1}=99\cdot {0.36363636363636365}^{10-1}=99\cdot {0.36363636363636365}^9=99\cdot 0.00011117464607063672=0.011006289960993036$$