সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=72$$ এবং সাধারণ অনুপাত: $$r=0.5138888888888888$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=72$$

$$a_2=a_1·r^{n-1}=72\cdot {0.5138888888888888}^{2-1}=72\cdot {0.5138888888888888}^1=72\cdot 0.5138888888888888=37$$

$$a_3=a_1·r^{n-1}=72\cdot {0.5138888888888888}^{3-1}=72\cdot {0.5138888888888888}^2=72\cdot 0.26408179012345673=19.013888888888886$$

$$a_4=a_1·r^{n-1}=72\cdot {0.5138888888888888}^{4-1}=72\cdot {0.5138888888888888}^3=72\cdot 0.13570869770233193=9.771026234567898$$

$$a_5=a_1·r^{n-1}=72\cdot {0.5138888888888888}^{5-1}=72\cdot {0.5138888888888888}^4=72\cdot 0.06973919187480945=5.021221814986281$$

$$a_6=a_1·r^{n-1}=72\cdot {0.5138888888888888}^{6-1}=72\cdot {0.5138888888888888}^5=72\cdot 0.03583819582455485=2.580350099367949$$

$$a_7=a_1·r^{n-1}=72\cdot {0.5138888888888888}^{7-1}=72\cdot {0.5138888888888888}^6=72\cdot 0.01841685063206291=1.3260132455085296$$

$$a_8=a_1·r^{n-1}=72\cdot {0.5138888888888888}^{8-1}=72\cdot {0.5138888888888888}^7=72\cdot 0.00946421490814344=0.6814234733863276$$

$$a_9=a_1·r^{n-1}=72\cdot {0.5138888888888888}^{9-1}=72\cdot {0.5138888888888888}^8=72\cdot 0.004863554883351489=0.3501759516013072$$

$$a_{10}=a_1·r^{n-1}=72\cdot {0.5138888888888888}^{10-1}=72\cdot {0.5138888888888888}^9=72\cdot 0.002499326815055626=0.17995153068400507$$