সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=99$$ এবং সাধারণ অনুপাত: $$r=1.3636363636363635$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=99$$

$$a_2=a_1·r^{n-1}=99\cdot {1.3636363636363635}^{2-1}=99\cdot {1.3636363636363635}^1=99\cdot 1.3636363636363635=135$$

$$a_3=a_1·r^{n-1}=99\cdot {1.3636363636363635}^{3-1}=99\cdot {1.3636363636363635}^2=99\cdot 1.8595041322314048=184.09090909090907$$

$$a_4=a_1·r^{n-1}=99\cdot {1.3636363636363635}^{4-1}=99\cdot {1.3636363636363635}^3=99\cdot 2.5356874530428244=251.03305785123962$$

$$a_5=a_1·r^{n-1}=99\cdot {1.3636363636363635}^{5-1}=99\cdot {1.3636363636363635}^4=99\cdot 3.4577556177856694=342.3178061607813$$

$$a_6=a_1·r^{n-1}=99\cdot {1.3636363636363635}^{6-1}=99\cdot {1.3636363636363635}^5=99\cdot 4.715121296980458=466.79700840106534$$

$$a_7=a_1·r^{n-1}=99\cdot {1.3636363636363635}^{7-1}=99\cdot {1.3636363636363635}^6=99\cdot 6.4297108595188055=636.5413750923617$$

$$a_8=a_1·r^{n-1}=99\cdot {1.3636363636363635}^{8-1}=99\cdot {1.3636363636363635}^7=99\cdot 8.76778753570746=868.0109660350387$$

$$a_9=a_1·r^{n-1}=99\cdot {1.3636363636363635}^{9-1}=99\cdot {1.3636363636363635}^8=99\cdot 11.956073912328357=1183.6513173205074$$

$$a_{10}=a_1·r^{n-1}=99\cdot {1.3636363636363635}^{10-1}=99\cdot {1.3636363636363635}^9=99\cdot 16.303737153175028=1614.0699781643277$$