সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=32$$ এবং সাধারণ অনুপাত: $$r=0.5625$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=32$$

$$a_2=a_1·r^{n-1}=32\cdot {0.5625}^{2-1}=32\cdot {0.5625}^1=32\cdot 0.5625=18$$

$$a_3=a_1·r^{n-1}=32\cdot {0.5625}^{3-1}=32\cdot {0.5625}^2=32\cdot 0.31640625=10.125$$

$$a_4=a_1·r^{n-1}=32\cdot {0.5625}^{4-1}=32\cdot {0.5625}^3=32\cdot 0.177978515625=5.6953125$$

$$a_5=a_1·r^{n-1}=32\cdot {0.5625}^{5-1}=32\cdot {0.5625}^4=32\cdot 0.1001129150390625=3.20361328125$$

$$a_6=a_1·r^{n-1}=32\cdot {0.5625}^{6-1}=32\cdot {0.5625}^5=32\cdot 0.056313514709472656=1.802032470703125$$

$$a_7=a_1·r^{n-1}=32\cdot {0.5625}^{7-1}=32\cdot {0.5625}^6=32\cdot 0.03167635202407837=1.0136432647705078$$

$$a_8=a_1·r^{n-1}=32\cdot {0.5625}^{8-1}=32\cdot {0.5625}^7=32\cdot 0.017817948013544083=0.5701743364334106$$

$$a_9=a_1·r^{n-1}=32\cdot {0.5625}^{9-1}=32\cdot {0.5625}^8=32\cdot 0.010022595757618546=0.3207230642437935$$

$$a_{10}=a_1·r^{n-1}=32\cdot {0.5625}^{10-1}=32\cdot {0.5625}^9=32\cdot 0.005637710113660432=0.18040672363713384$$