সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=80$$ এবং সাধারণ অনুপাত: $$r=0.9$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=80$$

$$a_2=a_1·r^{n-1}=80\cdot {0.9}^{2-1}=80\cdot {0.9}^1=80\cdot 0.9=72$$

$$a_3=a_1·r^{n-1}=80\cdot {0.9}^{3-1}=80\cdot {0.9}^2=80\cdot 0.81=64.80000000000001$$

$$a_4=a_1·r^{n-1}=80\cdot {0.9}^{4-1}=80\cdot {0.9}^3=80\cdot 0.7290000000000001=58.32000000000001$$

$$a_5=a_1·r^{n-1}=80\cdot {0.9}^{5-1}=80\cdot {0.9}^4=80\cdot 0.6561=52.488$$

$$a_6=a_1·r^{n-1}=80\cdot {0.9}^{6-1}=80\cdot {0.9}^5=80\cdot 0.5904900000000001=47.239200000000004$$

$$a_7=a_1·r^{n-1}=80\cdot {0.9}^{7-1}=80\cdot {0.9}^6=80\cdot 0.531441=42.515280000000004$$

$$a_8=a_1·r^{n-1}=80\cdot {0.9}^{8-1}=80\cdot {0.9}^7=80\cdot 0.4782969000000001=38.263752000000004$$

$$a_9=a_1·r^{n-1}=80\cdot {0.9}^{9-1}=80\cdot {0.9}^8=80\cdot 0.4304672100000001=34.43737680000001$$

$$a_{10}=a_1·r^{n-1}=80\cdot {0.9}^{10-1}=80\cdot {0.9}^9=80\cdot 0.3874204890000001=30.993639120000008$$