সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=13$$ এবং সাধারণ অনুপাত: $$r=1.4615384615384615$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=13$$

$$a_2=a_1·r^{n-1}=13\cdot {1.4615384615384615}^{2-1}=13\cdot {1.4615384615384615}^1=13\cdot 1.4615384615384615=19$$

$$a_3=a_1·r^{n-1}=13\cdot {1.4615384615384615}^{3-1}=13\cdot {1.4615384615384615}^2=13\cdot 2.1360946745562126=27.769230769230763$$

$$a_4=a_1·r^{n-1}=13\cdot {1.4615384615384615}^{4-1}=13\cdot {1.4615384615384615}^3=13\cdot 3.1219845243513875=40.58579881656804$$

$$a_5=a_1·r^{n-1}=13\cdot {1.4615384615384615}^{5-1}=13\cdot {1.4615384615384615}^4=13\cdot 4.5629004586674125=59.317705962676364$$

$$a_6=a_1·r^{n-1}=13\cdot {1.4615384615384615}^{6-1}=13\cdot {1.4615384615384615}^5=13\cdot 6.66885451651391=86.69510871468083$$

$$a_7=a_1·r^{n-1}=13\cdot {1.4615384615384615}^{7-1}=13\cdot {1.4615384615384615}^6=13\cdot 9.74678737028956=126.70823581376428$$

$$a_8=a_1·r^{n-1}=13\cdot {1.4615384615384615}^{8-1}=13\cdot {1.4615384615384615}^7=13\cdot 14.245304618115512=185.18896003550165$$

$$a_9=a_1·r^{n-1}=13\cdot {1.4615384615384615}^{9-1}=13\cdot {1.4615384615384615}^8=13\cdot 20.820060595707282=270.6607877441947$$

$$a_{10}=a_1·r^{n-1}=13\cdot {1.4615384615384615}^{10-1}=13\cdot {1.4615384615384615}^9=13\cdot 30.429319332187568=395.5811513184384$$