সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=55$$ এবং সাধারণ অনুপাত: $$r=0.6363636363636364$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=55$$

$$a_2=a_1·r^{n-1}=55\cdot {0.6363636363636364}^{2-1}=55\cdot {0.6363636363636364}^1=55\cdot 0.6363636363636364=35$$

$$a_3=a_1·r^{n-1}=55\cdot {0.6363636363636364}^{3-1}=55\cdot {0.6363636363636364}^2=55\cdot 0.4049586776859504=22.272727272727273$$

$$a_4=a_1·r^{n-1}=55\cdot {0.6363636363636364}^{4-1}=55\cdot {0.6363636363636364}^3=55\cdot 0.25770097670924114=14.173553719008263$$

$$a_5=a_1·r^{n-1}=55\cdot {0.6363636363636364}^{5-1}=55\cdot {0.6363636363636364}^4=55\cdot 0.16399153063315347=9.01953418482344$$

$$a_6=a_1·r^{n-1}=55\cdot {0.6363636363636364}^{6-1}=55\cdot {0.6363636363636364}^5=55\cdot 0.1043582467665522=5.739703572160371$$

$$a_7=a_1·r^{n-1}=55\cdot {0.6363636363636364}^{7-1}=55\cdot {0.6363636363636364}^6=55\cdot 0.06640979339689686=3.6525386368293273$$

$$a_8=a_1·r^{n-1}=55\cdot {0.6363636363636364}^{8-1}=55\cdot {0.6363636363636364}^7=55\cdot 0.04226077761620709=2.3243427688913902$$

$$a_9=a_1·r^{n-1}=55\cdot {0.6363636363636364}^{9-1}=55\cdot {0.6363636363636364}^8=55\cdot 0.026893222119404512=1.4791272165672482$$

$$a_{10}=a_1·r^{n-1}=55\cdot {0.6363636363636364}^{10-1}=55\cdot {0.6363636363636364}^9=55\cdot 0.017113868621439234=0.9412627741791579$$