সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=150$$ এবং সাধারণ অনুপাত: $$r=0.64$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=150$$

$$a_2=a_1·r^{n-1}=150\cdot {0.64}^{2-1}=150\cdot {0.64}^1=150\cdot 0.64=96$$

$$a_3=a_1·r^{n-1}=150\cdot {0.64}^{3-1}=150\cdot {0.64}^2=150\cdot 0.4096=61.440000000000005$$

$$a_4=a_1·r^{n-1}=150\cdot {0.64}^{4-1}=150\cdot {0.64}^3=150\cdot 0.26214400000000004=39.321600000000004$$

$$a_5=a_1·r^{n-1}=150\cdot {0.64}^{5-1}=150\cdot {0.64}^4=150\cdot 0.16777216=25.165824$$

$$a_6=a_1·r^{n-1}=150\cdot {0.64}^{6-1}=150\cdot {0.64}^5=150\cdot 0.10737418240000002=16.106127360000002$$

$$a_7=a_1·r^{n-1}=150\cdot {0.64}^{7-1}=150\cdot {0.64}^6=150\cdot 0.06871947673600001=10.307921510400002$$

$$a_8=a_1·r^{n-1}=150\cdot {0.64}^{8-1}=150\cdot {0.64}^7=150\cdot 0.04398046511104001=6.597069766656001$$

$$a_9=a_1·r^{n-1}=150\cdot {0.64}^{9-1}=150\cdot {0.64}^8=150\cdot 0.028147497671065606=4.222124650659841$$

$$a_{10}=a_1·r^{n-1}=150\cdot {0.64}^{10-1}=150\cdot {0.64}^9=150\cdot 0.01801439850948199=2.7021597764222984$$