সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=38$$ এবং সাধারণ অনুপাত: $$r=1.368421052631579$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=38$$

$$a_2=a_1·r^{n-1}=38\cdot {1.368421052631579}^{2-1}=38\cdot {1.368421052631579}^1=38\cdot 1.368421052631579=52$$

$$a_3=a_1·r^{n-1}=38\cdot {1.368421052631579}^{3-1}=38\cdot {1.368421052631579}^2=38\cdot 1.8725761772853187=71.15789473684211$$

$$a_4=a_1·r^{n-1}=38\cdot {1.368421052631579}^{4-1}=38\cdot {1.368421052631579}^3=38\cdot 2.562472663653594=97.37396121883657$$

$$a_5=a_1·r^{n-1}=38\cdot {1.368421052631579}^{5-1}=38\cdot {1.368421052631579}^4=38\cdot 3.506541539736497=133.24857850998688$$

$$a_6=a_1·r^{n-1}=38\cdot {1.368421052631579}^{6-1}=38\cdot {1.368421052631579}^5=38\cdot 4.798425264902575=182.34016006629787$$

$$a_7=a_1·r^{n-1}=38\cdot {1.368421052631579}^{7-1}=38\cdot {1.368421052631579}^6=38\cdot 6.566266151971945=249.5181137749339$$

$$a_8=a_1·r^{n-1}=38\cdot {1.368421052631579}^{8-1}=38\cdot {1.368421052631579}^7=38\cdot 8.985416839540557=341.44583990254114$$

$$a_9=a_1·r^{n-1}=38\cdot {1.368421052631579}^{9-1}=38\cdot {1.368421052631579}^8=38\cdot 12.295833569897605=467.24167565610895$$

$$a_{10}=a_1·r^{n-1}=38\cdot {1.368421052631579}^{10-1}=38\cdot {1.368421052631579}^9=38\cdot 16.825877516701986=639.3833456346755$$