সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=33$$ এবং সাধারণ অনুপাত: $$r=0.36363636363636365$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=33$$

$$a_2=a_1·r^{n-1}=33\cdot {0.36363636363636365}^{2-1}=33\cdot {0.36363636363636365}^1=33\cdot 0.36363636363636365=12$$

$$a_3=a_1·r^{n-1}=33\cdot {0.36363636363636365}^{3-1}=33\cdot {0.36363636363636365}^2=33\cdot 0.1322314049586777=4.363636363636363$$

$$a_4=a_1·r^{n-1}=33\cdot {0.36363636363636365}^{4-1}=33\cdot {0.36363636363636365}^3=33\cdot 0.04808414725770098=1.5867768595041323$$

$$a_5=a_1·r^{n-1}=33\cdot {0.36363636363636365}^{5-1}=33\cdot {0.36363636363636365}^4=33\cdot 0.01748514445734581=0.5770097670924118$$

$$a_6=a_1·r^{n-1}=33\cdot {0.36363636363636365}^{6-1}=33\cdot {0.36363636363636365}^5=33\cdot 0.0063582343481257495=0.20982173348814973$$

$$a_7=a_1·r^{n-1}=33\cdot {0.36363636363636365}^{7-1}=33\cdot {0.36363636363636365}^6=33\cdot 0.0023120852175002727=0.076298812177509$$

$$a_8=a_1·r^{n-1}=33\cdot {0.36363636363636365}^{8-1}=33\cdot {0.36363636363636365}^7=33\cdot 0.0008407582609091901=0.027745022610003275$$

$$a_9=a_1·r^{n-1}=33\cdot {0.36363636363636365}^{9-1}=33\cdot {0.36363636363636365}^8=33\cdot 0.00030573027669425094=0.010089099130910282$$

$$a_{10}=a_1·r^{n-1}=33\cdot {0.36363636363636365}^{10-1}=33\cdot {0.36363636363636365}^9=33\cdot 0.00011117464607063672=0.0036687633203310115$$