সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=125$$ এবং সাধারণ অনুপাত: $$r=0.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=125$$

$$a_2=a_1·r^{n-1}=125\cdot {0.6}^{2-1}=125\cdot {0.6}^1=125\cdot 0.6=75$$

$$a_3=a_1·r^{n-1}=125\cdot {0.6}^{3-1}=125\cdot {0.6}^2=125\cdot 0.36=45$$

$$a_4=a_1·r^{n-1}=125\cdot {0.6}^{4-1}=125\cdot {0.6}^3=125\cdot 0.21599999999999997=26.999999999999996$$

$$a_5=a_1·r^{n-1}=125\cdot {0.6}^{5-1}=125\cdot {0.6}^4=125\cdot 0.1296=16.2$$

$$a_6=a_1·r^{n-1}=125\cdot {0.6}^{6-1}=125\cdot {0.6}^5=125\cdot 0.07775999999999998=9.719999999999997$$

$$a_7=a_1·r^{n-1}=125\cdot {0.6}^{7-1}=125\cdot {0.6}^6=125\cdot 0.04665599999999999=5.831999999999999$$

$$a_8=a_1·r^{n-1}=125\cdot {0.6}^{8-1}=125\cdot {0.6}^7=125\cdot 0.027993599999999993=3.499199999999999$$

$$a_9=a_1·r^{n-1}=125\cdot {0.6}^{9-1}=125\cdot {0.6}^8=125\cdot 0.016796159999999994=2.099519999999999$$

$$a_{10}=a_1·r^{n-1}=125\cdot {0.6}^{10-1}=125\cdot {0.6}^9=125\cdot 0.010077695999999997=1.2597119999999997$$