সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=35$$ এবং সাধারণ অনুপাত: $$r=0.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=35$$

$$a_2=a_1·r^{n-1}=35\cdot {0.6}^{2-1}=35\cdot {0.6}^1=35\cdot 0.6=21$$

$$a_3=a_1·r^{n-1}=35\cdot {0.6}^{3-1}=35\cdot {0.6}^2=35\cdot 0.36=12.6$$

$$a_4=a_1·r^{n-1}=35\cdot {0.6}^{4-1}=35\cdot {0.6}^3=35\cdot 0.21599999999999997=7.559999999999999$$

$$a_5=a_1·r^{n-1}=35\cdot {0.6}^{5-1}=35\cdot {0.6}^4=35\cdot 0.1296=4.536$$

$$a_6=a_1·r^{n-1}=35\cdot {0.6}^{6-1}=35\cdot {0.6}^5=35\cdot 0.07775999999999998=2.7215999999999996$$

$$a_7=a_1·r^{n-1}=35\cdot {0.6}^{7-1}=35\cdot {0.6}^6=35\cdot 0.04665599999999999=1.6329599999999995$$

$$a_8=a_1·r^{n-1}=35\cdot {0.6}^{8-1}=35\cdot {0.6}^7=35\cdot 0.027993599999999993=0.9797759999999998$$

$$a_9=a_1·r^{n-1}=35\cdot {0.6}^{9-1}=35\cdot {0.6}^8=35\cdot 0.016796159999999994=0.5878655999999998$$

$$a_{10}=a_1·r^{n-1}=35\cdot {0.6}^{10-1}=35\cdot {0.6}^9=35\cdot 0.010077695999999997=0.3527193599999999$$