সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=30$$ এবং সাধারণ অনুপাত: $$r=4.5$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=30$$

$$a_2=a_1·r^{n-1}=30\cdot {4.5}^{2-1}=30\cdot {4.5}^1=30\cdot 4.5=135$$

$$a_3=a_1·r^{n-1}=30\cdot {4.5}^{3-1}=30\cdot {4.5}^2=30\cdot 20.25=607.5$$

$$a_4=a_1·r^{n-1}=30\cdot {4.5}^{4-1}=30\cdot {4.5}^3=30\cdot 91.125=2733.75$$

$$a_5=a_1·r^{n-1}=30\cdot {4.5}^{5-1}=30\cdot {4.5}^4=30\cdot 410.0625=12301.875$$

$$a_6=a_1·r^{n-1}=30\cdot {4.5}^{6-1}=30\cdot {4.5}^5=30\cdot 1845.28125=55358.4375$$

$$a_7=a_1·r^{n-1}=30\cdot {4.5}^{7-1}=30\cdot {4.5}^6=30\cdot 8303.765625=249112.96875$$

$$a_8=a_1·r^{n-1}=30\cdot {4.5}^{8-1}=30\cdot {4.5}^7=30\cdot 37366.9453125=1121008.359375$$

$$a_9=a_1·r^{n-1}=30\cdot {4.5}^{9-1}=30\cdot {4.5}^8=30\cdot 168151.25390625=5044537.6171875$$

$$a_{10}=a_1·r^{n-1}=30\cdot {4.5}^{10-1}=30\cdot {4.5}^9=30\cdot 756680.642578125=22700419.27734375$$