সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=30$$ এবং সাধারণ অনুপাত: $$r=0.3$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=30$$

$$a_2=a_1·r^{n-1}=30\cdot {0.3}^{2-1}=30\cdot {0.3}^1=30\cdot 0.3=9$$

$$a_3=a_1·r^{n-1}=30\cdot {0.3}^{3-1}=30\cdot {0.3}^2=30\cdot 0.09=2.6999999999999997$$

$$a_4=a_1·r^{n-1}=30\cdot {0.3}^{4-1}=30\cdot {0.3}^3=30\cdot 0.026999999999999996=0.8099999999999998$$

$$a_5=a_1·r^{n-1}=30\cdot {0.3}^{5-1}=30\cdot {0.3}^4=30\cdot 0.0081=0.243$$

$$a_6=a_1·r^{n-1}=30\cdot {0.3}^{6-1}=30\cdot {0.3}^5=30\cdot 0.0024299999999999994=0.07289999999999998$$

$$a_7=a_1·r^{n-1}=30\cdot {0.3}^{7-1}=30\cdot {0.3}^6=30\cdot 0.0007289999999999998=0.021869999999999994$$

$$a_8=a_1·r^{n-1}=30\cdot {0.3}^{8-1}=30\cdot {0.3}^7=30\cdot 0.00021869999999999995=0.006560999999999998$$

$$a_9=a_1·r^{n-1}=30\cdot {0.3}^{9-1}=30\cdot {0.3}^8=30\cdot 6.560999999999998E-05=0.0019682999999999992$$

$$a_{10}=a_1·r^{n-1}=30\cdot {0.3}^{10-1}=30\cdot {0.3}^9=30\cdot 1.9682999999999994E-05=0.0005904899999999998$$