সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=480$$ এবং সাধারণ অনুপাত: $$r=0.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=480$$

$$a_2=a_1·r^{n-1}=480\cdot {0.6}^{2-1}=480\cdot {0.6}^1=480\cdot 0.6=288$$

$$a_3=a_1·r^{n-1}=480\cdot {0.6}^{3-1}=480\cdot {0.6}^2=480\cdot 0.36=172.79999999999998$$

$$a_4=a_1·r^{n-1}=480\cdot {0.6}^{4-1}=480\cdot {0.6}^3=480\cdot 0.21599999999999997=103.67999999999998$$

$$a_5=a_1·r^{n-1}=480\cdot {0.6}^{5-1}=480\cdot {0.6}^4=480\cdot 0.1296=62.208$$

$$a_6=a_1·r^{n-1}=480\cdot {0.6}^{6-1}=480\cdot {0.6}^5=480\cdot 0.07775999999999998=37.32479999999999$$

$$a_7=a_1·r^{n-1}=480\cdot {0.6}^{7-1}=480\cdot {0.6}^6=480\cdot 0.04665599999999999=22.394879999999993$$

$$a_8=a_1·r^{n-1}=480\cdot {0.6}^{8-1}=480\cdot {0.6}^7=480\cdot 0.027993599999999993=13.436927999999996$$

$$a_9=a_1·r^{n-1}=480\cdot {0.6}^{9-1}=480\cdot {0.6}^8=480\cdot 0.016796159999999994=8.062156799999997$$

$$a_{10}=a_1·r^{n-1}=480\cdot {0.6}^{10-1}=480\cdot {0.6}^9=480\cdot 0.010077695999999997=4.837294079999999$$