সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=300$$ এবং সাধারণ অনুপাত: $$r=0.48$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=300$$

$$a_2=a_1·r^{n-1}=300\cdot {0.48}^{2-1}=300\cdot {0.48}^1=300\cdot 0.48=144$$

$$a_3=a_1·r^{n-1}=300\cdot {0.48}^{3-1}=300\cdot {0.48}^2=300\cdot 0.2304=69.12$$

$$a_4=a_1·r^{n-1}=300\cdot {0.48}^{4-1}=300\cdot {0.48}^3=300\cdot 0.11059199999999998=33.17759999999999$$

$$a_5=a_1·r^{n-1}=300\cdot {0.48}^{5-1}=300\cdot {0.48}^4=300\cdot 0.05308415999999999=15.925247999999998$$

$$a_6=a_1·r^{n-1}=300\cdot {0.48}^{6-1}=300\cdot {0.48}^5=300\cdot 0.025480396799999996=7.644119039999999$$

$$a_7=a_1·r^{n-1}=300\cdot {0.48}^{7-1}=300\cdot {0.48}^6=300\cdot 0.012230590463999998=3.6691771391999994$$

$$a_8=a_1·r^{n-1}=300\cdot {0.48}^{8-1}=300\cdot {0.48}^7=300\cdot 0.0058706834227199986=1.7612050268159996$$

$$a_9=a_1·r^{n-1}=300\cdot {0.48}^{9-1}=300\cdot {0.48}^8=300\cdot 0.002817928042905599=0.8453784128716797$$

$$a_{10}=a_1·r^{n-1}=300\cdot {0.48}^{10-1}=300\cdot {0.48}^9=300\cdot 0.0013526054605946876=0.4057816381784063$$