সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=2,100$$ এবং সাধারণ অনুপাত: $$r=0.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=2100$$

$$a_2=a_1·r^{n-1}=2100\cdot {0.6}^{2-1}=2100\cdot {0.6}^1=2100\cdot 0.6=1260$$

$$a_3=a_1·r^{n-1}=2100\cdot {0.6}^{3-1}=2100\cdot {0.6}^2=2100\cdot 0.36=756$$

$$a_4=a_1·r^{n-1}=2100\cdot {0.6}^{4-1}=2100\cdot {0.6}^3=2100\cdot 0.21599999999999997=453.5999999999999$$

$$a_5=a_1·r^{n-1}=2100\cdot {0.6}^{5-1}=2100\cdot {0.6}^4=2100\cdot 0.1296=272.15999999999997$$

$$a_6=a_1·r^{n-1}=2100\cdot {0.6}^{6-1}=2100\cdot {0.6}^5=2100\cdot 0.07775999999999998=163.29599999999996$$

$$a_7=a_1·r^{n-1}=2100\cdot {0.6}^{7-1}=2100\cdot {0.6}^6=2100\cdot 0.04665599999999999=97.97759999999998$$

$$a_8=a_1·r^{n-1}=2100\cdot {0.6}^{8-1}=2100\cdot {0.6}^7=2100\cdot 0.027993599999999993=58.78655999999999$$

$$a_9=a_1·r^{n-1}=2100\cdot {0.6}^{9-1}=2100\cdot {0.6}^8=2100\cdot 0.016796159999999994=35.27193599999999$$

$$a_{10}=a_1·r^{n-1}=2100\cdot {0.6}^{10-1}=2100\cdot {0.6}^9=2100\cdot 0.010077695999999997=21.163161599999995$$