সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=300$$ এবং সাধারণ অনুপাত: $$r=0.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=300$$

$$a_2=a_1·r^{n-1}=300\cdot {0.6}^{2-1}=300\cdot {0.6}^1=300\cdot 0.6=180$$

$$a_3=a_1·r^{n-1}=300\cdot {0.6}^{3-1}=300\cdot {0.6}^2=300\cdot 0.36=108$$

$$a_4=a_1·r^{n-1}=300\cdot {0.6}^{4-1}=300\cdot {0.6}^3=300\cdot 0.21599999999999997=64.8$$

$$a_5=a_1·r^{n-1}=300\cdot {0.6}^{5-1}=300\cdot {0.6}^4=300\cdot 0.1296=38.879999999999995$$

$$a_6=a_1·r^{n-1}=300\cdot {0.6}^{6-1}=300\cdot {0.6}^5=300\cdot 0.07775999999999998=23.327999999999996$$

$$a_7=a_1·r^{n-1}=300\cdot {0.6}^{7-1}=300\cdot {0.6}^6=300\cdot 0.04665599999999999=13.996799999999997$$

$$a_8=a_1·r^{n-1}=300\cdot {0.6}^{8-1}=300\cdot {0.6}^7=300\cdot 0.027993599999999993=8.398079999999998$$

$$a_9=a_1·r^{n-1}=300\cdot {0.6}^{9-1}=300\cdot {0.6}^8=300\cdot 0.016796159999999994=5.038847999999998$$

$$a_{10}=a_1·r^{n-1}=300\cdot {0.6}^{10-1}=300\cdot {0.6}^9=300\cdot 0.010077695999999997=3.0233087999999992$$