সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=108$$ এবং সাধারণ অনুপাত: $$r=4.5$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=108$$

$$a_2=a_1·r^{n-1}=108\cdot {4.5}^{2-1}=108\cdot {4.5}^1=108\cdot 4.5=486$$

$$a_3=a_1·r^{n-1}=108\cdot {4.5}^{3-1}=108\cdot {4.5}^2=108\cdot 20.25=2187$$

$$a_4=a_1·r^{n-1}=108\cdot {4.5}^{4-1}=108\cdot {4.5}^3=108\cdot 91.125=9841.5$$

$$a_5=a_1·r^{n-1}=108\cdot {4.5}^{5-1}=108\cdot {4.5}^4=108\cdot 410.0625=44286.75$$

$$a_6=a_1·r^{n-1}=108\cdot {4.5}^{6-1}=108\cdot {4.5}^5=108\cdot 1845.28125=199290.375$$

$$a_7=a_1·r^{n-1}=108\cdot {4.5}^{7-1}=108\cdot {4.5}^6=108\cdot 8303.765625=896806.6875$$

$$a_8=a_1·r^{n-1}=108\cdot {4.5}^{8-1}=108\cdot {4.5}^7=108\cdot 37366.9453125=4035630.09375$$

$$a_9=a_1·r^{n-1}=108\cdot {4.5}^{9-1}=108\cdot {4.5}^8=108\cdot 168151.25390625=18160335.421875$$

$$a_{10}=a_1·r^{n-1}=108\cdot {4.5}^{10-1}=108\cdot {4.5}^9=108\cdot 756680.642578125=81721509.3984375$$