সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=55$$ এবং সাধারণ অনুপাত: $$r=0.7636363636363637$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=55$$

$$a_2=a_1·r^{n-1}=55\cdot {0.7636363636363637}^{2-1}=55\cdot {0.7636363636363637}^1=55\cdot 0.7636363636363637=42$$

$$a_3=a_1·r^{n-1}=55\cdot {0.7636363636363637}^{3-1}=55\cdot {0.7636363636363637}^2=55\cdot 0.5831404958677686=32.07272727272727$$

$$a_4=a_1·r^{n-1}=55\cdot {0.7636363636363637}^{4-1}=55\cdot {0.7636363636363637}^3=55\cdot 0.4453072877535688=24.491900826446283$$

$$a_5=a_1·r^{n-1}=55\cdot {0.7636363636363637}^{5-1}=55\cdot {0.7636363636363637}^4=55\cdot 0.3400528379209071=18.702906085649893$$

$$a_6=a_1·r^{n-1}=55\cdot {0.7636363636363637}^{6-1}=55\cdot {0.7636363636363637}^5=55\cdot 0.25967671259414726=14.282219192678099$$

$$a_7=a_1·r^{n-1}=55\cdot {0.7636363636363637}^{7-1}=55\cdot {0.7636363636363637}^6=55\cdot 0.19829858052643973=10.906421928954185$$

$$a_8=a_1·r^{n-1}=55\cdot {0.7636363636363637}^{8-1}=55\cdot {0.7636363636363637}^7=55\cdot 0.15142800694746308=8.32854038211047$$

$$a_9=a_1·r^{n-1}=55\cdot {0.7636363636363637}^{9-1}=55\cdot {0.7636363636363637}^8=55\cdot 0.11563593257806272=6.3599762917934495$$

$$a_{10}=a_1·r^{n-1}=55\cdot {0.7636363636363637}^{10-1}=55\cdot {0.7636363636363637}^9=55\cdot 0.08830380305961152=4.856709168278634$$