সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=30$$ এবং সাধারণ অনুপাত: $$r=1.8$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=30$$

$$a_2=a_1·r^{n-1}=30\cdot {1.8}^{2-1}=30\cdot {1.8}^1=30\cdot 1.8=54$$

$$a_3=a_1·r^{n-1}=30\cdot {1.8}^{3-1}=30\cdot {1.8}^2=30\cdot 3.24=97.2$$

$$a_4=a_1·r^{n-1}=30\cdot {1.8}^{4-1}=30\cdot {1.8}^3=30\cdot 5.832000000000001=174.96000000000004$$

$$a_5=a_1·r^{n-1}=30\cdot {1.8}^{5-1}=30\cdot {1.8}^4=30\cdot 10.4976=314.928$$

$$a_6=a_1·r^{n-1}=30\cdot {1.8}^{6-1}=30\cdot {1.8}^5=30\cdot 18.895680000000002=566.8704$$

$$a_7=a_1·r^{n-1}=30\cdot {1.8}^{7-1}=30\cdot {1.8}^6=30\cdot 34.012224=1020.3667200000001$$

$$a_8=a_1·r^{n-1}=30\cdot {1.8}^{8-1}=30\cdot {1.8}^7=30\cdot 61.22200320000001=1836.6600960000003$$

$$a_9=a_1·r^{n-1}=30\cdot {1.8}^{9-1}=30\cdot {1.8}^8=30\cdot 110.19960576000003=3305.988172800001$$

$$a_{10}=a_1·r^{n-1}=30\cdot {1.8}^{10-1}=30\cdot {1.8}^9=30\cdot 198.35929036800005=5950.778711040001$$