সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=65$$ এবং সাধারণ অনুপাত: $$r=0.6461538461538462$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=65$$

$$a_2=a_1·r^{n-1}=65\cdot {0.6461538461538462}^{2-1}=65\cdot {0.6461538461538462}^1=65\cdot 0.6461538461538462=42$$

$$a_3=a_1·r^{n-1}=65\cdot {0.6461538461538462}^{3-1}=65\cdot {0.6461538461538462}^2=65\cdot 0.41751479289940835=27.13846153846154$$

$$a_4=a_1·r^{n-1}=65\cdot {0.6461538461538462}^{4-1}=65\cdot {0.6461538461538462}^3=65\cdot 0.26977878925807924=17.53562130177515$$

$$a_5=a_1·r^{n-1}=65\cdot {0.6461538461538462}^{5-1}=65\cdot {0.6461538461538462}^4=65\cdot 0.17431860228983584=11.330709148839329$$

$$a_6=a_1·r^{n-1}=65\cdot {0.6461538461538462}^{6-1}=65\cdot {0.6461538461538462}^5=65\cdot 0.11263663532574009=7.321381296173105$$

$$a_7=a_1·r^{n-1}=65\cdot {0.6461538461538462}^{7-1}=65\cdot {0.6461538461538462}^6=65\cdot 0.07278059513355513=4.730738683681083$$

$$a_8=a_1·r^{n-1}=65\cdot {0.6461538461538462}^{8-1}=65\cdot {0.6461538461538462}^7=65\cdot 0.04702746147091255=3.056784995609316$$

$$a_9=a_1·r^{n-1}=65\cdot {0.6461538461538462}^{9-1}=65\cdot {0.6461538461538462}^8=65\cdot 0.030386975104281958=1.9751533817783273$$

$$a_{10}=a_1·r^{n-1}=65\cdot {0.6461538461538462}^{10-1}=65\cdot {0.6461538461538462}^9=65\cdot 0.019634660836612958=1.2762529543798422$$