সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=65$$ এবং সাধারণ অনুপাত: $$r=0.4153846153846154$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=65$$

$$a_2=a_1·r^{n-1}=65\cdot {0.4153846153846154}^{2-1}=65\cdot {0.4153846153846154}^1=65\cdot 0.4153846153846154=27$$

$$a_3=a_1·r^{n-1}=65\cdot {0.4153846153846154}^{3-1}=65\cdot {0.4153846153846154}^2=65\cdot 0.17254437869822487=11.215384615384616$$

$$a_4=a_1·r^{n-1}=65\cdot {0.4153846153846154}^{4-1}=65\cdot {0.4153846153846154}^3=65\cdot 0.07167228038233957=4.658698224852072$$

$$a_5=a_1·r^{n-1}=65\cdot {0.4153846153846154}^{5-1}=65\cdot {0.4153846153846154}^4=65\cdot 0.029771562620356438=1.9351515703231685$$

$$a_6=a_1·r^{n-1}=65\cdot {0.4153846153846154}^{6-1}=65\cdot {0.4153846153846154}^5=65\cdot 0.012366649088455752=0.8038321907496239$$

$$a_7=a_1·r^{n-1}=65\cdot {0.4153846153846154}^{7-1}=65\cdot {0.4153846153846154}^6=65\cdot 0.005136915775204697=0.3338995253883053$$

$$a_8=a_1·r^{n-1}=65\cdot {0.4153846153846154}^{8-1}=65\cdot {0.4153846153846154}^7=65\cdot 0.0021337957835465666=0.13869672593052682$$

$$a_9=a_1·r^{n-1}=65\cdot {0.4153846153846154}^{9-1}=65\cdot {0.4153846153846154}^8=65\cdot 0.0008863459408578046=0.0576124861557573$$

$$a_{10}=a_1·r^{n-1}=65\cdot {0.4153846153846154}^{10-1}=65\cdot {0.4153846153846154}^9=65\cdot 0.00036817446774093423=0.023931340403160726$$