সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=130$$ এবং সাধারণ অনুপাত: $$r=0.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=130$$

$$a_2=a_1·r^{n-1}=130\cdot {0.6}^{2-1}=130\cdot {0.6}^1=130\cdot 0.6=78$$

$$a_3=a_1·r^{n-1}=130\cdot {0.6}^{3-1}=130\cdot {0.6}^2=130\cdot 0.36=46.8$$

$$a_4=a_1·r^{n-1}=130\cdot {0.6}^{4-1}=130\cdot {0.6}^3=130\cdot 0.21599999999999997=28.079999999999995$$

$$a_5=a_1·r^{n-1}=130\cdot {0.6}^{5-1}=130\cdot {0.6}^4=130\cdot 0.1296=16.848$$

$$a_6=a_1·r^{n-1}=130\cdot {0.6}^{6-1}=130\cdot {0.6}^5=130\cdot 0.07775999999999998=10.108799999999997$$

$$a_7=a_1·r^{n-1}=130\cdot {0.6}^{7-1}=130\cdot {0.6}^6=130\cdot 0.04665599999999999=6.065279999999999$$

$$a_8=a_1·r^{n-1}=130\cdot {0.6}^{8-1}=130\cdot {0.6}^7=130\cdot 0.027993599999999993=3.6391679999999993$$

$$a_9=a_1·r^{n-1}=130\cdot {0.6}^{9-1}=130\cdot {0.6}^8=130\cdot 0.016796159999999994=2.183500799999999$$

$$a_{10}=a_1·r^{n-1}=130\cdot {0.6}^{10-1}=130\cdot {0.6}^9=130\cdot 0.010077695999999997=1.3101004799999996$$