সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=375$$ এবং সাধারণ অনুপাত: $$r=0.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=375$$

$$a_2=a_1·r^{n-1}=375\cdot {0.6}^{2-1}=375\cdot {0.6}^1=375\cdot 0.6=225$$

$$a_3=a_1·r^{n-1}=375\cdot {0.6}^{3-1}=375\cdot {0.6}^2=375\cdot 0.36=135$$

$$a_4=a_1·r^{n-1}=375\cdot {0.6}^{4-1}=375\cdot {0.6}^3=375\cdot 0.21599999999999997=80.99999999999999$$

$$a_5=a_1·r^{n-1}=375\cdot {0.6}^{5-1}=375\cdot {0.6}^4=375\cdot 0.1296=48.599999999999994$$

$$a_6=a_1·r^{n-1}=375\cdot {0.6}^{6-1}=375\cdot {0.6}^5=375\cdot 0.07775999999999998=29.159999999999993$$

$$a_7=a_1·r^{n-1}=375\cdot {0.6}^{7-1}=375\cdot {0.6}^6=375\cdot 0.04665599999999999=17.495999999999995$$

$$a_8=a_1·r^{n-1}=375\cdot {0.6}^{8-1}=375\cdot {0.6}^7=375\cdot 0.027993599999999993=10.497599999999997$$

$$a_9=a_1·r^{n-1}=375\cdot {0.6}^{9-1}=375\cdot {0.6}^8=375\cdot 0.016796159999999994=6.2985599999999975$$

$$a_{10}=a_1·r^{n-1}=375\cdot {0.6}^{10-1}=375\cdot {0.6}^9=375\cdot 0.010077695999999997=3.779135999999999$$