সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=90$$ এবং সাধারণ অনুপাত: $$r=0.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=90$$

$$a_2=a_1·r^{n-1}=90\cdot {0.6}^{2-1}=90\cdot {0.6}^1=90\cdot 0.6=54$$

$$a_3=a_1·r^{n-1}=90\cdot {0.6}^{3-1}=90\cdot {0.6}^2=90\cdot 0.36=32.4$$

$$a_4=a_1·r^{n-1}=90\cdot {0.6}^{4-1}=90\cdot {0.6}^3=90\cdot 0.21599999999999997=19.439999999999998$$

$$a_5=a_1·r^{n-1}=90\cdot {0.6}^{5-1}=90\cdot {0.6}^4=90\cdot 0.1296=11.664$$

$$a_6=a_1·r^{n-1}=90\cdot {0.6}^{6-1}=90\cdot {0.6}^5=90\cdot 0.07775999999999998=6.998399999999998$$

$$a_7=a_1·r^{n-1}=90\cdot {0.6}^{7-1}=90\cdot {0.6}^6=90\cdot 0.04665599999999999=4.199039999999999$$

$$a_8=a_1·r^{n-1}=90\cdot {0.6}^{8-1}=90\cdot {0.6}^7=90\cdot 0.027993599999999993=2.5194239999999994$$

$$a_9=a_1·r^{n-1}=90\cdot {0.6}^{9-1}=90\cdot {0.6}^8=90\cdot 0.016796159999999994=1.5116543999999994$$

$$a_{10}=a_1·r^{n-1}=90\cdot {0.6}^{10-1}=90\cdot {0.6}^9=90\cdot 0.010077695999999997=0.9069926399999997$$