সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=83$$ এবং সাধারণ অনুপাত: $$r=0.7228915662650602$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=83$$

$$a_2=a_1·r^{n-1}=83\cdot {0.7228915662650602}^{2-1}=83\cdot {0.7228915662650602}^1=83\cdot 0.7228915662650602=60$$

$$a_3=a_1·r^{n-1}=83\cdot {0.7228915662650602}^{3-1}=83\cdot {0.7228915662650602}^2=83\cdot 0.522572216577152=43.37349397590362$$

$$a_4=a_1·r^{n-1}=83\cdot {0.7228915662650602}^{4-1}=83\cdot {0.7228915662650602}^3=83\cdot 0.37776304812806166=31.354332994629118$$

$$a_5=a_1·r^{n-1}=83\cdot {0.7228915662650602}^{5-1}=83\cdot {0.7228915662650602}^4=83\cdot 0.27308172153835786=22.6657828876837$$

$$a_6=a_1·r^{n-1}=83\cdot {0.7228915662650602}^{6-1}=83\cdot {0.7228915662650602}^5=83\cdot 0.19740847340122253=16.38490329230147$$

$$a_7=a_1·r^{n-1}=83\cdot {0.7228915662650602}^{7-1}=83\cdot {0.7228915662650602}^6=83\cdot 0.14270492053100423=11.84450840407335$$

$$a_8=a_1·r^{n-1}=83\cdot {0.7228915662650602}^{8-1}=83\cdot {0.7228915662650602}^7=83\cdot 0.1031601835163886=8.562295231860254$$

$$a_9=a_1·r^{n-1}=83\cdot {0.7228915662650602}^{9-1}=83\cdot {0.7228915662650602}^8=83\cdot 0.07457362663835321=6.189611010983317$$

$$a_{10}=a_1·r^{n-1}=83\cdot {0.7228915662650602}^{10-1}=83\cdot {0.7228915662650602}^9=83\cdot 0.05390864576266497=4.4744175983011925$$