সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=-33$$ এবং সাধারণ অনুপাত: $$r=1.8181818181818181$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=-33$$

$$a_2=a_1·r^{n-1}=-33\cdot {1.8181818181818181}^{2-1}=-33\cdot {1.8181818181818181}^1=-33\cdot 1.8181818181818181=-60$$

$$a_3=a_1·r^{n-1}=-33\cdot {1.8181818181818181}^{3-1}=-33\cdot {1.8181818181818181}^2=-33\cdot 3.305785123966942=-109.09090909090908$$

$$a_4=a_1·r^{n-1}=-33\cdot {1.8181818181818181}^{4-1}=-33\cdot {1.8181818181818181}^3=-33\cdot 6.010518407212621=-198.3471074380165$$

$$a_5=a_1·r^{n-1}=-33\cdot {1.8181818181818181}^{5-1}=-33\cdot {1.8181818181818181}^4=-33\cdot 10.92821528584113=-360.6311044327573$$

$$a_6=a_1·r^{n-1}=-33\cdot {1.8181818181818181}^{6-1}=-33\cdot {1.8181818181818181}^5=-33\cdot 19.86948233789296=-655.6929171504677$$

$$a_7=a_1·r^{n-1}=-33\cdot {1.8181818181818181}^{7-1}=-33\cdot {1.8181818181818181}^6=-33\cdot 36.12633152344175=-1192.1689402735776$$

$$a_8=a_1·r^{n-1}=-33\cdot {1.8181818181818181}^{8-1}=-33\cdot {1.8181818181818181}^7=-33\cdot 65.68423913353045=-2167.579891406505$$

$$a_9=a_1·r^{n-1}=-33\cdot {1.8181818181818181}^{9-1}=-33\cdot {1.8181818181818181}^8=-33\cdot 119.42588933369173=-3941.054348011827$$

$$a_{10}=a_1·r^{n-1}=-33\cdot {1.8181818181818181}^{10-1}=-33\cdot {1.8181818181818181}^9=-33\cdot 217.1379806067122=-7165.553360021503$$