সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=55$$ এবং সাধারণ অনুপাত: $$r=0.9090909090909091$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=55$$

$$a_2=a_1·r^{n-1}=55\cdot {0.9090909090909091}^{2-1}=55\cdot {0.9090909090909091}^1=55\cdot 0.9090909090909091=50$$

$$a_3=a_1·r^{n-1}=55\cdot {0.9090909090909091}^{3-1}=55\cdot {0.9090909090909091}^2=55\cdot 0.8264462809917354=45.45454545454545$$

$$a_4=a_1·r^{n-1}=55\cdot {0.9090909090909091}^{4-1}=55\cdot {0.9090909090909091}^3=55\cdot 0.7513148009015777=41.32231404958677$$

$$a_5=a_1·r^{n-1}=55\cdot {0.9090909090909091}^{5-1}=55\cdot {0.9090909090909091}^4=55\cdot 0.6830134553650706=37.56574004507888$$

$$a_6=a_1·r^{n-1}=55\cdot {0.9090909090909091}^{6-1}=55\cdot {0.9090909090909091}^5=55\cdot 0.620921323059155=34.15067276825353$$

$$a_7=a_1·r^{n-1}=55\cdot {0.9090909090909091}^{7-1}=55\cdot {0.9090909090909091}^6=55\cdot 0.5644739300537773=31.046066152957753$$

$$a_8=a_1·r^{n-1}=55\cdot {0.9090909090909091}^{8-1}=55\cdot {0.9090909090909091}^7=55\cdot 0.5131581182307067=28.223696502688867$$

$$a_9=a_1·r^{n-1}=55\cdot {0.9090909090909091}^{9-1}=55\cdot {0.9090909090909091}^8=55\cdot 0.4665073802097333=25.657905911535334$$

$$a_{10}=a_1·r^{n-1}=55\cdot {0.9090909090909091}^{10-1}=55\cdot {0.9090909090909091}^9=55\cdot 0.4240976183724848=23.325369010486664$$