সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=85$$ এবং সাধারণ অনুপাত: $$r=0.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=85$$

$$a_2=a_1·r^{n-1}=85\cdot {0.6}^{2-1}=85\cdot {0.6}^1=85\cdot 0.6=51$$

$$a_3=a_1·r^{n-1}=85\cdot {0.6}^{3-1}=85\cdot {0.6}^2=85\cdot 0.36=30.599999999999998$$

$$a_4=a_1·r^{n-1}=85\cdot {0.6}^{4-1}=85\cdot {0.6}^3=85\cdot 0.21599999999999997=18.359999999999996$$

$$a_5=a_1·r^{n-1}=85\cdot {0.6}^{5-1}=85\cdot {0.6}^4=85\cdot 0.1296=11.016$$

$$a_6=a_1·r^{n-1}=85\cdot {0.6}^{6-1}=85\cdot {0.6}^5=85\cdot 0.07775999999999998=6.609599999999999$$

$$a_7=a_1·r^{n-1}=85\cdot {0.6}^{7-1}=85\cdot {0.6}^6=85\cdot 0.04665599999999999=3.965759999999999$$

$$a_8=a_1·r^{n-1}=85\cdot {0.6}^{8-1}=85\cdot {0.6}^7=85\cdot 0.027993599999999993=2.3794559999999993$$

$$a_9=a_1·r^{n-1}=85\cdot {0.6}^{9-1}=85\cdot {0.6}^8=85\cdot 0.016796159999999994=1.4276735999999994$$

$$a_{10}=a_1·r^{n-1}=85\cdot {0.6}^{10-1}=85\cdot {0.6}^9=85\cdot 0.010077695999999997=0.8566041599999997$$