সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=50$$ এবং সাধারণ অনুপাত: $$r=0.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=50$$

$$a_2=a_1·r^{n-1}=50\cdot {0.6}^{2-1}=50\cdot {0.6}^1=50\cdot 0.6=30$$

$$a_3=a_1·r^{n-1}=50\cdot {0.6}^{3-1}=50\cdot {0.6}^2=50\cdot 0.36=18$$

$$a_4=a_1·r^{n-1}=50\cdot {0.6}^{4-1}=50\cdot {0.6}^3=50\cdot 0.21599999999999997=10.799999999999999$$

$$a_5=a_1·r^{n-1}=50\cdot {0.6}^{5-1}=50\cdot {0.6}^4=50\cdot 0.1296=6.4799999999999995$$

$$a_6=a_1·r^{n-1}=50\cdot {0.6}^{6-1}=50\cdot {0.6}^5=50\cdot 0.07775999999999998=3.887999999999999$$

$$a_7=a_1·r^{n-1}=50\cdot {0.6}^{7-1}=50\cdot {0.6}^6=50\cdot 0.04665599999999999=2.3327999999999993$$

$$a_8=a_1·r^{n-1}=50\cdot {0.6}^{8-1}=50\cdot {0.6}^7=50\cdot 0.027993599999999993=1.3996799999999996$$

$$a_9=a_1·r^{n-1}=50\cdot {0.6}^{9-1}=50\cdot {0.6}^8=50\cdot 0.016796159999999994=0.8398079999999997$$

$$a_{10}=a_1·r^{n-1}=50\cdot {0.6}^{10-1}=50\cdot {0.6}^9=50\cdot 0.010077695999999997=0.5038847999999998$$