সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=30$$ এবং সাধারণ অনুপাত: $$r=0.9$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=30$$

$$a_2=a_1·r^{n-1}=30\cdot {0.9}^{2-1}=30\cdot {0.9}^1=30\cdot 0.9=27$$

$$a_3=a_1·r^{n-1}=30\cdot {0.9}^{3-1}=30\cdot {0.9}^2=30\cdot 0.81=24.3$$

$$a_4=a_1·r^{n-1}=30\cdot {0.9}^{4-1}=30\cdot {0.9}^3=30\cdot 0.7290000000000001=21.870000000000005$$

$$a_5=a_1·r^{n-1}=30\cdot {0.9}^{5-1}=30\cdot {0.9}^4=30\cdot 0.6561=19.683$$

$$a_6=a_1·r^{n-1}=30\cdot {0.9}^{6-1}=30\cdot {0.9}^5=30\cdot 0.5904900000000001=17.7147$$

$$a_7=a_1·r^{n-1}=30\cdot {0.9}^{7-1}=30\cdot {0.9}^6=30\cdot 0.531441=15.943230000000002$$

$$a_8=a_1·r^{n-1}=30\cdot {0.9}^{8-1}=30\cdot {0.9}^7=30\cdot 0.4782969000000001=14.348907000000002$$

$$a_9=a_1·r^{n-1}=30\cdot {0.9}^{9-1}=30\cdot {0.9}^8=30\cdot 0.4304672100000001=12.914016300000004$$

$$a_{10}=a_1·r^{n-1}=30\cdot {0.9}^{10-1}=30\cdot {0.9}^9=30\cdot 0.3874204890000001=11.622614670000003$$