সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=75$$ এবং সাধারণ অনুপাত: $$r=1.8$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {1.8}^{2-1}=75\cdot {1.8}^1=75\cdot 1.8=135$$

$$a_3=a_1·r^{n-1}=75\cdot {1.8}^{3-1}=75\cdot {1.8}^2=75\cdot 3.24=243.00000000000003$$

$$a_4=a_1·r^{n-1}=75\cdot {1.8}^{4-1}=75\cdot {1.8}^3=75\cdot 5.832000000000001=437.40000000000003$$

$$a_5=a_1·r^{n-1}=75\cdot {1.8}^{5-1}=75\cdot {1.8}^4=75\cdot 10.4976=787.32$$

$$a_6=a_1·r^{n-1}=75\cdot {1.8}^{6-1}=75\cdot {1.8}^5=75\cdot 18.895680000000002=1417.1760000000002$$

$$a_7=a_1·r^{n-1}=75\cdot {1.8}^{7-1}=75\cdot {1.8}^6=75\cdot 34.012224=2550.9168000000004$$

$$a_8=a_1·r^{n-1}=75\cdot {1.8}^{8-1}=75\cdot {1.8}^7=75\cdot 61.22200320000001=4591.650240000001$$

$$a_9=a_1·r^{n-1}=75\cdot {1.8}^{9-1}=75\cdot {1.8}^8=75\cdot 110.19960576000003=8264.970432000002$$

$$a_{10}=a_1·r^{n-1}=75\cdot {1.8}^{10-1}=75\cdot {1.8}^9=75\cdot 198.35929036800005=14876.946777600004$$