সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=65$$ এবং সাধারণ অনুপাত: $$r=1.8$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=65$$

$$a_2=a_1·r^{n-1}=65\cdot {1.8}^{2-1}=65\cdot {1.8}^1=65\cdot 1.8=117$$

$$a_3=a_1·r^{n-1}=65\cdot {1.8}^{3-1}=65\cdot {1.8}^2=65\cdot 3.24=210.60000000000002$$

$$a_4=a_1·r^{n-1}=65\cdot {1.8}^{4-1}=65\cdot {1.8}^3=65\cdot 5.832000000000001=379.08000000000004$$

$$a_5=a_1·r^{n-1}=65\cdot {1.8}^{5-1}=65\cdot {1.8}^4=65\cdot 10.4976=682.344$$

$$a_6=a_1·r^{n-1}=65\cdot {1.8}^{6-1}=65\cdot {1.8}^5=65\cdot 18.895680000000002=1228.2192000000002$$

$$a_7=a_1·r^{n-1}=65\cdot {1.8}^{7-1}=65\cdot {1.8}^6=65\cdot 34.012224=2210.7945600000003$$

$$a_8=a_1·r^{n-1}=65\cdot {1.8}^{8-1}=65\cdot {1.8}^7=65\cdot 61.22200320000001=3979.4302080000007$$

$$a_9=a_1·r^{n-1}=65\cdot {1.8}^{9-1}=65\cdot {1.8}^8=65\cdot 110.19960576000003=7162.974374400002$$

$$a_{10}=a_1·r^{n-1}=65\cdot {1.8}^{10-1}=65\cdot {1.8}^9=65\cdot 198.35929036800005=12893.353873920003$$