সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=64$$ এবং সাধারণ অনুপাত: $$r=0.25$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=64$$

$$a_2=a_1·r^{n-1}=64\cdot {0.25}^{2-1}=64\cdot {0.25}^1=64\cdot 0.25=16$$

$$a_3=a_1·r^{n-1}=64\cdot {0.25}^{3-1}=64\cdot {0.25}^2=64\cdot 0.0625=4$$

$$a_4=a_1·r^{n-1}=64\cdot {0.25}^{4-1}=64\cdot {0.25}^3=64\cdot 0.015625=1$$

$$a_5=a_1·r^{n-1}=64\cdot {0.25}^{5-1}=64\cdot {0.25}^4=64\cdot 0.00390625=0.25$$

$$a_6=a_1·r^{n-1}=64\cdot {0.25}^{6-1}=64\cdot {0.25}^5=64\cdot 0.0009765625=0.0625$$

$$a_7=a_1·r^{n-1}=64\cdot {0.25}^{7-1}=64\cdot {0.25}^6=64\cdot 0.000244140625=0.015625$$

$$a_8=a_1·r^{n-1}=64\cdot {0.25}^{8-1}=64\cdot {0.25}^7=64\cdot 6.103515625E-05=0.00390625$$

$$a_9=a_1·r^{n-1}=64\cdot {0.25}^{9-1}=64\cdot {0.25}^8=64\cdot 1.52587890625E-05=0.0009765625$$

$$a_{10}=a_1·r^{n-1}=64\cdot {0.25}^{10-1}=64\cdot {0.25}^9=64\cdot 3.814697265625E-06=0.000244140625$$