সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=100$$ এবং সাধারণ অনুপাত: $$r=1.3$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=100$$

$$a_2=a_1·r^{n-1}=100\cdot {1.3}^{2-1}=100\cdot {1.3}^1=100\cdot 1.3=130$$

$$a_3=a_1·r^{n-1}=100\cdot {1.3}^{3-1}=100\cdot {1.3}^2=100\cdot 1.6900000000000002=169.00000000000003$$

$$a_4=a_1·r^{n-1}=100\cdot {1.3}^{4-1}=100\cdot {1.3}^3=100\cdot 2.197=219.70000000000002$$

$$a_5=a_1·r^{n-1}=100\cdot {1.3}^{5-1}=100\cdot {1.3}^4=100\cdot 2.8561000000000005=285.61000000000007$$

$$a_6=a_1·r^{n-1}=100\cdot {1.3}^{6-1}=100\cdot {1.3}^5=100\cdot 3.7129300000000005=371.29300000000006$$

$$a_7=a_1·r^{n-1}=100\cdot {1.3}^{7-1}=100\cdot {1.3}^6=100\cdot 4.826809000000001=482.68090000000007$$

$$a_8=a_1·r^{n-1}=100\cdot {1.3}^{8-1}=100\cdot {1.3}^7=100\cdot 6.274851700000002=627.4851700000002$$

$$a_9=a_1·r^{n-1}=100\cdot {1.3}^{9-1}=100\cdot {1.3}^8=100\cdot 8.157307210000003=815.7307210000002$$

$$a_{10}=a_1·r^{n-1}=100\cdot {1.3}^{10-1}=100\cdot {1.3}^9=100\cdot 10.604499373000003=1060.4499373000003$$