সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=99$$ এবং সাধারণ অনুপাত: $$r=0.7272727272727273$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=99$$

$$a_2=a_1·r^{n-1}=99\cdot {0.7272727272727273}^{2-1}=99\cdot {0.7272727272727273}^1=99\cdot 0.7272727272727273=72$$

$$a_3=a_1·r^{n-1}=99\cdot {0.7272727272727273}^{3-1}=99\cdot {0.7272727272727273}^2=99\cdot 0.5289256198347108=52.36363636363637$$

$$a_4=a_1·r^{n-1}=99\cdot {0.7272727272727273}^{4-1}=99\cdot {0.7272727272727273}^3=99\cdot 0.38467317806160783=38.082644628099175$$

$$a_5=a_1·r^{n-1}=99\cdot {0.7272727272727273}^{5-1}=99\cdot {0.7272727272727273}^4=99\cdot 0.279762311317533=27.696468820435765$$

$$a_6=a_1·r^{n-1}=99\cdot {0.7272727272727273}^{6-1}=99\cdot {0.7272727272727273}^5=99\cdot 0.20346349914002398=20.142886414862375$$

$$a_7=a_1·r^{n-1}=99\cdot {0.7272727272727273}^{7-1}=99\cdot {0.7272727272727273}^6=99\cdot 0.14797345392001746=14.649371938081728$$

$$a_8=a_1·r^{n-1}=99\cdot {0.7272727272727273}^{8-1}=99\cdot {0.7272727272727273}^7=99\cdot 0.10761705739637634=10.654088682241257$$

$$a_9=a_1·r^{n-1}=99\cdot {0.7272727272727273}^{9-1}=99\cdot {0.7272727272727273}^8=99\cdot 0.07826695083372824=7.748428132539096$$

$$a_{10}=a_1·r^{n-1}=99\cdot {0.7272727272727273}^{10-1}=99\cdot {0.7272727272727273}^9=99\cdot 0.056921418788166=5.635220460028434$$