সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=60$$ এবং সাধারণ অনুপাত: $$r=4.5$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=60$$

$$a_2=a_1·r^{n-1}=60\cdot {4.5}^{2-1}=60\cdot {4.5}^1=60\cdot 4.5=270$$

$$a_3=a_1·r^{n-1}=60\cdot {4.5}^{3-1}=60\cdot {4.5}^2=60\cdot 20.25=1215$$

$$a_4=a_1·r^{n-1}=60\cdot {4.5}^{4-1}=60\cdot {4.5}^3=60\cdot 91.125=5467.5$$

$$a_5=a_1·r^{n-1}=60\cdot {4.5}^{5-1}=60\cdot {4.5}^4=60\cdot 410.0625=24603.75$$

$$a_6=a_1·r^{n-1}=60\cdot {4.5}^{6-1}=60\cdot {4.5}^5=60\cdot 1845.28125=110716.875$$

$$a_7=a_1·r^{n-1}=60\cdot {4.5}^{7-1}=60\cdot {4.5}^6=60\cdot 8303.765625=498225.9375$$

$$a_8=a_1·r^{n-1}=60\cdot {4.5}^{8-1}=60\cdot {4.5}^7=60\cdot 37366.9453125=2242016.71875$$

$$a_9=a_1·r^{n-1}=60\cdot {4.5}^{9-1}=60\cdot {4.5}^8=60\cdot 168151.25390625=10089075.234375$$

$$a_{10}=a_1·r^{n-1}=60\cdot {4.5}^{10-1}=60\cdot {4.5}^9=60\cdot 756680.642578125=45400838.5546875$$