সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=245$$ এবং সাধারণ অনুপাত: $$r=0.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=245$$

$$a_2=a_1·r^{n-1}=245\cdot {0.6}^{2-1}=245\cdot {0.6}^1=245\cdot 0.6=147$$

$$a_3=a_1·r^{n-1}=245\cdot {0.6}^{3-1}=245\cdot {0.6}^2=245\cdot 0.36=88.2$$

$$a_4=a_1·r^{n-1}=245\cdot {0.6}^{4-1}=245\cdot {0.6}^3=245\cdot 0.21599999999999997=52.919999999999995$$

$$a_5=a_1·r^{n-1}=245\cdot {0.6}^{5-1}=245\cdot {0.6}^4=245\cdot 0.1296=31.752$$

$$a_6=a_1·r^{n-1}=245\cdot {0.6}^{6-1}=245\cdot {0.6}^5=245\cdot 0.07775999999999998=19.051199999999994$$

$$a_7=a_1·r^{n-1}=245\cdot {0.6}^{7-1}=245\cdot {0.6}^6=245\cdot 0.04665599999999999=11.430719999999997$$

$$a_8=a_1·r^{n-1}=245\cdot {0.6}^{8-1}=245\cdot {0.6}^7=245\cdot 0.027993599999999993=6.858431999999999$$

$$a_9=a_1·r^{n-1}=245\cdot {0.6}^{9-1}=245\cdot {0.6}^8=245\cdot 0.016796159999999994=4.115059199999998$$

$$a_{10}=a_1·r^{n-1}=245\cdot {0.6}^{10-1}=245\cdot {0.6}^9=245\cdot 0.010077695999999997=2.4690355199999994$$