সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=65$$ এবং সাধারণ অনুপাত: $$r=0.46153846153846156$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=65$$

$$a_2=a_1·r^{n-1}=65\cdot {0.46153846153846156}^{2-1}=65\cdot {0.46153846153846156}^1=65\cdot 0.46153846153846156=30$$

$$a_3=a_1·r^{n-1}=65\cdot {0.46153846153846156}^{3-1}=65\cdot {0.46153846153846156}^2=65\cdot 0.21301775147928997=13.846153846153848$$

$$a_4=a_1·r^{n-1}=65\cdot {0.46153846153846156}^{4-1}=65\cdot {0.46153846153846156}^3=65\cdot 0.09831588529813383=6.390532544378699$$

$$a_5=a_1·r^{n-1}=65\cdot {0.46153846153846156}^{5-1}=65\cdot {0.46153846153846156}^4=65\cdot 0.04537656244529254=2.9494765589440153$$

$$a_6=a_1·r^{n-1}=65\cdot {0.46153846153846156}^{6-1}=65\cdot {0.46153846153846156}^5=65\cdot 0.02094302882090425=1.3612968733587762$$

$$a_7=a_1·r^{n-1}=65\cdot {0.46153846153846156}^{7-1}=65\cdot {0.46153846153846156}^6=65\cdot 0.009666013301955809=0.6282908646271276$$

$$a_8=a_1·r^{n-1}=65\cdot {0.46153846153846156}^{8-1}=65\cdot {0.46153846153846156}^7=65\cdot 0.004461236908594989=0.2899803990586743$$

$$a_9=a_1·r^{n-1}=65\cdot {0.46153846153846156}^{9-1}=65\cdot {0.46153846153846156}^8=65\cdot 0.0020590324193515337=0.1338371072578497$$

$$a_{10}=a_1·r^{n-1}=65\cdot {0.46153846153846156}^{10-1}=65\cdot {0.46153846153846156}^9=65\cdot 0.0009503226550853232=0.06177097258054601$$