সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=52$$ এবং সাধারণ অনুপাত: $$r=1.4615384615384615$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=52$$

$$a_2=a_1·r^{n-1}=52\cdot {1.4615384615384615}^{2-1}=52\cdot {1.4615384615384615}^1=52\cdot 1.4615384615384615=76$$

$$a_3=a_1·r^{n-1}=52\cdot {1.4615384615384615}^{3-1}=52\cdot {1.4615384615384615}^2=52\cdot 2.1360946745562126=111.07692307692305$$

$$a_4=a_1·r^{n-1}=52\cdot {1.4615384615384615}^{4-1}=52\cdot {1.4615384615384615}^3=52\cdot 3.1219845243513875=162.34319526627215$$

$$a_5=a_1·r^{n-1}=52\cdot {1.4615384615384615}^{5-1}=52\cdot {1.4615384615384615}^4=52\cdot 4.5629004586674125=237.27082385070545$$

$$a_6=a_1·r^{n-1}=52\cdot {1.4615384615384615}^{6-1}=52\cdot {1.4615384615384615}^5=52\cdot 6.66885451651391=346.7804348587233$$

$$a_7=a_1·r^{n-1}=52\cdot {1.4615384615384615}^{7-1}=52\cdot {1.4615384615384615}^6=52\cdot 9.74678737028956=506.8329432550571$$

$$a_8=a_1·r^{n-1}=52\cdot {1.4615384615384615}^{8-1}=52\cdot {1.4615384615384615}^7=52\cdot 14.245304618115512=740.7558401420066$$

$$a_9=a_1·r^{n-1}=52\cdot {1.4615384615384615}^{9-1}=52\cdot {1.4615384615384615}^8=52\cdot 20.820060595707282=1082.6431509767788$$

$$a_{10}=a_1·r^{n-1}=52\cdot {1.4615384615384615}^{10-1}=52\cdot {1.4615384615384615}^9=52\cdot 30.429319332187568=1582.3246052737536$$