সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=65$$ এবং সাধারণ অনুপাত: $$r=1.4615384615384615$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=65$$

$$a_2=a_1·r^{n-1}=65\cdot {1.4615384615384615}^{2-1}=65\cdot {1.4615384615384615}^1=65\cdot 1.4615384615384615=95$$

$$a_3=a_1·r^{n-1}=65\cdot {1.4615384615384615}^{3-1}=65\cdot {1.4615384615384615}^2=65\cdot 2.1360946745562126=138.8461538461538$$

$$a_4=a_1·r^{n-1}=65\cdot {1.4615384615384615}^{4-1}=65\cdot {1.4615384615384615}^3=65\cdot 3.1219845243513875=202.92899408284018$$

$$a_5=a_1·r^{n-1}=65\cdot {1.4615384615384615}^{5-1}=65\cdot {1.4615384615384615}^4=65\cdot 4.5629004586674125=296.5885298133818$$

$$a_6=a_1·r^{n-1}=65\cdot {1.4615384615384615}^{6-1}=65\cdot {1.4615384615384615}^5=65\cdot 6.66885451651391=433.4755435734042$$

$$a_7=a_1·r^{n-1}=65\cdot {1.4615384615384615}^{7-1}=65\cdot {1.4615384615384615}^6=65\cdot 9.74678737028956=633.5411790688214$$

$$a_8=a_1·r^{n-1}=65\cdot {1.4615384615384615}^{8-1}=65\cdot {1.4615384615384615}^7=65\cdot 14.245304618115512=925.9448001775082$$

$$a_9=a_1·r^{n-1}=65\cdot {1.4615384615384615}^{9-1}=65\cdot {1.4615384615384615}^8=65\cdot 20.820060595707282=1353.3039387209733$$

$$a_{10}=a_1·r^{n-1}=65\cdot {1.4615384615384615}^{10-1}=65\cdot {1.4615384615384615}^9=65\cdot 30.429319332187568=1977.905756592192$$