সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=30$$ এবং সাধারণ অনুপাত: $$r=4.2$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=30$$

$$a_2=a_1·r^{n-1}=30\cdot {4.2}^{2-1}=30\cdot {4.2}^1=30\cdot 4.2=126$$

$$a_3=a_1·r^{n-1}=30\cdot {4.2}^{3-1}=30\cdot {4.2}^2=30\cdot 17.64=529.2$$

$$a_4=a_1·r^{n-1}=30\cdot {4.2}^{4-1}=30\cdot {4.2}^3=30\cdot 74.08800000000001=2222.6400000000003$$

$$a_5=a_1·r^{n-1}=30\cdot {4.2}^{5-1}=30\cdot {4.2}^4=30\cdot 311.16960000000006=9335.088000000002$$

$$a_6=a_1·r^{n-1}=30\cdot {4.2}^{6-1}=30\cdot {4.2}^5=30\cdot 1306.9123200000004=39207.36960000001$$

$$a_7=a_1·r^{n-1}=30\cdot {4.2}^{7-1}=30\cdot {4.2}^6=30\cdot 5489.031744000002=164670.95232000004$$

$$a_8=a_1·r^{n-1}=30\cdot {4.2}^{8-1}=30\cdot {4.2}^7=30\cdot 23053.933324800008=691617.9997440003$$

$$a_9=a_1·r^{n-1}=30\cdot {4.2}^{9-1}=30\cdot {4.2}^8=30\cdot 96826.51996416003=2904795.598924801$$

$$a_{10}=a_1·r^{n-1}=30\cdot {4.2}^{10-1}=30\cdot {4.2}^9=30\cdot 406671.38384947216=12200141.515484165$$