সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=5$$ এবং সাধারণ অনুপাত: $$r=0.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=5$$

$$a_2=a_1·r^{n-1}=5\cdot {0.6}^{2-1}=5\cdot {0.6}^1=5\cdot 0.6=3$$

$$a_3=a_1·r^{n-1}=5\cdot {0.6}^{3-1}=5\cdot {0.6}^2=5\cdot 0.36=1.7999999999999998$$

$$a_4=a_1·r^{n-1}=5\cdot {0.6}^{4-1}=5\cdot {0.6}^3=5\cdot 0.21599999999999997=1.0799999999999998$$

$$a_5=a_1·r^{n-1}=5\cdot {0.6}^{5-1}=5\cdot {0.6}^4=5\cdot 0.1296=0.6479999999999999$$

$$a_6=a_1·r^{n-1}=5\cdot {0.6}^{6-1}=5\cdot {0.6}^5=5\cdot 0.07775999999999998=0.3887999999999999$$

$$a_7=a_1·r^{n-1}=5\cdot {0.6}^{7-1}=5\cdot {0.6}^6=5\cdot 0.04665599999999999=0.23327999999999993$$

$$a_8=a_1·r^{n-1}=5\cdot {0.6}^{8-1}=5\cdot {0.6}^7=5\cdot 0.027993599999999993=0.13996799999999998$$

$$a_9=a_1·r^{n-1}=5\cdot {0.6}^{9-1}=5\cdot {0.6}^8=5\cdot 0.016796159999999994=0.08398079999999997$$

$$a_{10}=a_1·r^{n-1}=5\cdot {0.6}^{10-1}=5\cdot {0.6}^9=5\cdot 0.010077695999999997=0.050388479999999986$$