সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=57$$ এবং সাধারণ অনুপাত: $$r=0.8421052631578947$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=57$$

$$a_2=a_1·r^{n-1}=57\cdot {0.8421052631578947}^{2-1}=57\cdot {0.8421052631578947}^1=57\cdot 0.8421052631578947=48$$

$$a_3=a_1·r^{n-1}=57\cdot {0.8421052631578947}^{3-1}=57\cdot {0.8421052631578947}^2=57\cdot 0.709141274238227=40.42105263157894$$

$$a_4=a_1·r^{n-1}=57\cdot {0.8421052631578947}^{4-1}=57\cdot {0.8421052631578947}^3=57\cdot 0.5971715993585069=34.0387811634349$$

$$a_5=a_1·r^{n-1}=57\cdot {0.8421052631578947}^{5-1}=57\cdot {0.8421052631578947}^4=57\cdot 0.5028813468282164=28.664236769208333$$

$$a_6=a_1·r^{n-1}=57\cdot {0.8421052631578947}^{6-1}=57\cdot {0.8421052631578947}^5=57\cdot 0.4234790289079717=24.138304647754385$$

$$a_7=a_1·r^{n-1}=57\cdot {0.8421052631578947}^{7-1}=57\cdot {0.8421052631578947}^6=57\cdot 0.3566139190803972=20.32699338758264$$

$$a_8=a_1·r^{n-1}=57\cdot {0.8421052631578947}^{8-1}=57\cdot {0.8421052631578947}^7=57\cdot 0.30030645817296603=17.117468115859065$$

$$a_9=a_1·r^{n-1}=57\cdot {0.8421052631578947}^{9-1}=57\cdot {0.8421052631578947}^8=57\cdot 0.25288964898776084=14.414709992302368$$

$$a_{10}=a_1·r^{n-1}=57\cdot {0.8421052631578947}^{10-1}=57\cdot {0.8421052631578947}^9=57\cdot 0.21295970441074596=12.13870315141252$$