সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=90$$ এবং সাধারণ অনুপাত: $$r=0.3888888888888889$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=90$$

$$a_2=a_1·r^{n-1}=90\cdot {0.3888888888888889}^{2-1}=90\cdot {0.3888888888888889}^1=90\cdot 0.3888888888888889=35$$

$$a_3=a_1·r^{n-1}=90\cdot {0.3888888888888889}^{3-1}=90\cdot {0.3888888888888889}^2=90\cdot 0.15123456790123457=13.61111111111111$$

$$a_4=a_1·r^{n-1}=90\cdot {0.3888888888888889}^{4-1}=90\cdot {0.3888888888888889}^3=90\cdot 0.05881344307270234=5.2932098765432105$$

$$a_5=a_1·r^{n-1}=90\cdot {0.3888888888888889}^{5-1}=90\cdot {0.3888888888888889}^4=90\cdot 0.02287189452827313=2.0584705075445817$$

$$a_6=a_1·r^{n-1}=90\cdot {0.3888888888888889}^{6-1}=90\cdot {0.3888888888888889}^5=90\cdot 0.008894625649883995=0.8005163084895596$$

$$a_7=a_1·r^{n-1}=90\cdot {0.3888888888888889}^{7-1}=90\cdot {0.3888888888888889}^6=90\cdot 0.003459021086065998=0.3113118977459398$$

$$a_8=a_1·r^{n-1}=90\cdot {0.3888888888888889}^{8-1}=90\cdot {0.3888888888888889}^7=90\cdot 0.0013451748668034439=0.12106573801230995$$

$$a_9=a_1·r^{n-1}=90\cdot {0.3888888888888889}^{9-1}=90\cdot {0.3888888888888889}^8=90\cdot 0.0005231235593124503=0.04708112033812053$$

$$a_{10}=a_1·r^{n-1}=90\cdot {0.3888888888888889}^{10-1}=90\cdot {0.3888888888888889}^9=90\cdot 0.00020343693973261958=0.018309324575935763$$