সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=550$$ এবং সাধারণ অনুপাত: $$r=0.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=550$$

$$a_2=a_1·r^{n-1}=550\cdot {0.6}^{2-1}=550\cdot {0.6}^1=550\cdot 0.6=330$$

$$a_3=a_1·r^{n-1}=550\cdot {0.6}^{3-1}=550\cdot {0.6}^2=550\cdot 0.36=198$$

$$a_4=a_1·r^{n-1}=550\cdot {0.6}^{4-1}=550\cdot {0.6}^3=550\cdot 0.21599999999999997=118.79999999999998$$

$$a_5=a_1·r^{n-1}=550\cdot {0.6}^{5-1}=550\cdot {0.6}^4=550\cdot 0.1296=71.28$$

$$a_6=a_1·r^{n-1}=550\cdot {0.6}^{6-1}=550\cdot {0.6}^5=550\cdot 0.07775999999999998=42.767999999999994$$

$$a_7=a_1·r^{n-1}=550\cdot {0.6}^{7-1}=550\cdot {0.6}^6=550\cdot 0.04665599999999999=25.660799999999995$$

$$a_8=a_1·r^{n-1}=550\cdot {0.6}^{8-1}=550\cdot {0.6}^7=550\cdot 0.027993599999999993=15.396479999999997$$

$$a_9=a_1·r^{n-1}=550\cdot {0.6}^{9-1}=550\cdot {0.6}^8=550\cdot 0.016796159999999994=9.237887999999996$$

$$a_{10}=a_1·r^{n-1}=550\cdot {0.6}^{10-1}=550\cdot {0.6}^9=550\cdot 0.010077695999999997=5.542732799999999$$