সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=20$$ এবং সাধারণ অনুপাত: $$r=3.8$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=20$$

$$a_2=a_1·r^{n-1}=20\cdot {3.8}^{2-1}=20\cdot {3.8}^1=20\cdot 3.8=76$$

$$a_3=a_1·r^{n-1}=20\cdot {3.8}^{3-1}=20\cdot {3.8}^2=20\cdot 14.44=288.8$$

$$a_4=a_1·r^{n-1}=20\cdot {3.8}^{4-1}=20\cdot {3.8}^3=20\cdot 54.87199999999999=1097.4399999999998$$

$$a_5=a_1·r^{n-1}=20\cdot {3.8}^{5-1}=20\cdot {3.8}^4=20\cdot 208.51359999999997=4170.271999999999$$

$$a_6=a_1·r^{n-1}=20\cdot {3.8}^{6-1}=20\cdot {3.8}^5=20\cdot 792.3516799999998=15847.033599999995$$

$$a_7=a_1·r^{n-1}=20\cdot {3.8}^{7-1}=20\cdot {3.8}^6=20\cdot 3010.936383999999=60218.72767999998$$

$$a_8=a_1·r^{n-1}=20\cdot {3.8}^{8-1}=20\cdot {3.8}^7=20\cdot 11441.558259199996=228831.16518399992$$

$$a_9=a_1·r^{n-1}=20\cdot {3.8}^{9-1}=20\cdot {3.8}^8=20\cdot 43477.921384959984=869558.4276991996$$

$$a_{10}=a_1·r^{n-1}=20\cdot {3.8}^{10-1}=20\cdot {3.8}^9=20\cdot 165216.10126284792=3304322.0252569583$$