সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=78$$ এবং সাধারণ অনুপাত: $$r=54.38461538461539$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=78$$

$$a_2=a_1·r^{n-1}=78\cdot {54.38461538461539}^{2-1}=78\cdot {54.38461538461539}^1=78\cdot 54.38461538461539=4242$$

$$a_3=a_1·r^{n-1}=78\cdot {54.38461538461539}^{3-1}=78\cdot {54.38461538461539}^2=78\cdot 2957.6863905325445=230699.53846153847$$

$$a_4=a_1·r^{n-1}=78\cdot {54.38461538461539}^{4-1}=78\cdot {54.38461538461539}^3=78\cdot 160852.6367774238=12546505.668639056$$

$$a_5=a_1·r^{n-1}=78\cdot {54.38461538461539}^{5-1}=78\cdot {54.38461538461539}^4=78\cdot 8747908.784741431=682336885.2098317$$

$$a_6=a_1·r^{n-1}=78\cdot {54.38461538461539}^{6-1}=78\cdot {54.38461538461539}^5=78\cdot 475751654.677861=37108629064.87315$$

$$a_7=a_1·r^{n-1}=78\cdot {54.38461538461539}^{7-1}=78\cdot {54.38461538461539}^6=78\cdot 25873570758.249825=2018138519143.4863$$

$$a_8=a_1·r^{n-1}=78\cdot {54.38461538461539}^{8-1}=78\cdot {54.38461538461539}^7=78\cdot 1407124194314.0483=109755687156495.77$$

$$a_9=a_1·r^{n-1}=78\cdot {54.38461538461539}^{9-1}=78\cdot {54.38461538461539}^8=78\cdot 76525908106156.31=5969020832280192$$

$$a_{10}=a_1·r^{n-1}=78\cdot {54.38461538461539}^{10-1}=78\cdot {54.38461538461539}^9=78\cdot 4161832079311732=3.246229021863151E+17$$