সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=64$$ এবং সাধারণ অনুপাত: $$r=0.8125$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=64$$

$$a_2=a_1·r^{n-1}=64\cdot {0.8125}^{2-1}=64\cdot {0.8125}^1=64\cdot 0.8125=52$$

$$a_3=a_1·r^{n-1}=64\cdot {0.8125}^{3-1}=64\cdot {0.8125}^2=64\cdot 0.66015625=42.25$$

$$a_4=a_1·r^{n-1}=64\cdot {0.8125}^{4-1}=64\cdot {0.8125}^3=64\cdot 0.536376953125=34.328125$$

$$a_5=a_1·r^{n-1}=64\cdot {0.8125}^{5-1}=64\cdot {0.8125}^4=64\cdot 0.4358062744140625=27.8916015625$$

$$a_6=a_1·r^{n-1}=64\cdot {0.8125}^{6-1}=64\cdot {0.8125}^5=64\cdot 0.3540925979614258=22.66192626953125$$

$$a_7=a_1·r^{n-1}=64\cdot {0.8125}^{7-1}=64\cdot {0.8125}^6=64\cdot 0.28770023584365845=18.41281509399414$$

$$a_8=a_1·r^{n-1}=64\cdot {0.8125}^{8-1}=64\cdot {0.8125}^7=64\cdot 0.2337564416229725=14.96041226387024$$

$$a_9=a_1·r^{n-1}=64\cdot {0.8125}^{9-1}=64\cdot {0.8125}^8=64\cdot 0.18992710881866515=12.15533496439457$$

$$a_{10}=a_1·r^{n-1}=64\cdot {0.8125}^{10-1}=64\cdot {0.8125}^9=64\cdot 0.15431577591516543=9.876209658570588$$