সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=30$$ এবং সাধারণ অনুপাত: $$r=0.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=30$$

$$a_2=a_1·r^{n-1}=30\cdot {0.6}^{2-1}=30\cdot {0.6}^1=30\cdot 0.6=18$$

$$a_3=a_1·r^{n-1}=30\cdot {0.6}^{3-1}=30\cdot {0.6}^2=30\cdot 0.36=10.799999999999999$$

$$a_4=a_1·r^{n-1}=30\cdot {0.6}^{4-1}=30\cdot {0.6}^3=30\cdot 0.21599999999999997=6.479999999999999$$

$$a_5=a_1·r^{n-1}=30\cdot {0.6}^{5-1}=30\cdot {0.6}^4=30\cdot 0.1296=3.888$$

$$a_6=a_1·r^{n-1}=30\cdot {0.6}^{6-1}=30\cdot {0.6}^5=30\cdot 0.07775999999999998=2.3327999999999993$$

$$a_7=a_1·r^{n-1}=30\cdot {0.6}^{7-1}=30\cdot {0.6}^6=30\cdot 0.04665599999999999=1.3996799999999996$$

$$a_8=a_1·r^{n-1}=30\cdot {0.6}^{8-1}=30\cdot {0.6}^7=30\cdot 0.027993599999999993=0.8398079999999998$$

$$a_9=a_1·r^{n-1}=30\cdot {0.6}^{9-1}=30\cdot {0.6}^8=30\cdot 0.016796159999999994=0.5038847999999998$$

$$a_{10}=a_1·r^{n-1}=30\cdot {0.6}^{10-1}=30\cdot {0.6}^9=30\cdot 0.010077695999999997=0.3023308799999999$$