সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=1,125$$ এবং সাধারণ অনুপাত: $$r=1.8$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=1125$$

$$a_2=a_1·r^{n-1}=1125\cdot {1.8}^{2-1}=1125\cdot {1.8}^1=1125\cdot 1.8=2025$$

$$a_3=a_1·r^{n-1}=1125\cdot {1.8}^{3-1}=1125\cdot {1.8}^2=1125\cdot 3.24=3645.0000000000005$$

$$a_4=a_1·r^{n-1}=1125\cdot {1.8}^{4-1}=1125\cdot {1.8}^3=1125\cdot 5.832000000000001=6561.000000000001$$

$$a_5=a_1·r^{n-1}=1125\cdot {1.8}^{5-1}=1125\cdot {1.8}^4=1125\cdot 10.4976=11809.800000000001$$

$$a_6=a_1·r^{n-1}=1125\cdot {1.8}^{6-1}=1125\cdot {1.8}^5=1125\cdot 18.895680000000002=21257.640000000003$$

$$a_7=a_1·r^{n-1}=1125\cdot {1.8}^{7-1}=1125\cdot {1.8}^6=1125\cdot 34.012224=38263.752$$

$$a_8=a_1·r^{n-1}=1125\cdot {1.8}^{8-1}=1125\cdot {1.8}^7=1125\cdot 61.22200320000001=68874.75360000001$$

$$a_9=a_1·r^{n-1}=1125\cdot {1.8}^{9-1}=1125\cdot {1.8}^8=1125\cdot 110.19960576000003=123974.55648000003$$

$$a_{10}=a_1·r^{n-1}=1125\cdot {1.8}^{10-1}=1125\cdot {1.8}^9=1125\cdot 198.35929036800005=223154.20166400005$$