সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=69$$ এবং সাধারণ অনুপাত: $$r=1.4202898550724639$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=69$$

$$a_2=a_1·r^{n-1}=69\cdot {1.4202898550724639}^{2-1}=69\cdot {1.4202898550724639}^1=69\cdot 1.4202898550724639=98$$

$$a_3=a_1·r^{n-1}=69\cdot {1.4202898550724639}^{3-1}=69\cdot {1.4202898550724639}^2=69\cdot 2.0172232724217602=139.18840579710147$$

$$a_4=a_1·r^{n-1}=69\cdot {1.4202898550724639}^{4-1}=69\cdot {1.4202898550724639}^3=69\cdot 2.8650417492367035=197.68788069733253$$

$$a_5=a_1·r^{n-1}=69\cdot {1.4202898550724639}^{5-1}=69\cdot {1.4202898550724639}^4=69\cdot 4.069189730799955=280.7740914251969$$

$$a_6=a_1·r^{n-1}=69\cdot {1.4202898550724639}^{6-1}=69\cdot {1.4202898550724639}^5=69\cdot 5.779428893020228=398.7805936183957$$

$$a_7=a_1·r^{n-1}=69\cdot {1.4202898550724639}^{7-1}=69\cdot {1.4202898550724639}^6=69\cdot 8.208464224869308=566.3840315159823$$

$$a_8=a_1·r^{n-1}=69\cdot {1.4202898550724639}^{8-1}=69\cdot {1.4202898550724639}^7=69\cdot 11.658398464307135=804.4294940371923$$

$$a_9=a_1·r^{n-1}=69\cdot {1.4202898550724639}^{9-1}=69\cdot {1.4202898550724639}^8=69\cdot 16.558305065247815=1142.5230495020992$$

$$a_{10}=a_1·r^{n-1}=69\cdot {1.4202898550724639}^{10-1}=69\cdot {1.4202898550724639}^9=69\cdot 23.517592701366464=1622.713896394286$$