সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=54$$ এবং সাধারণ অনুপাত: $$r=1.1851851851851851$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=54$$

$$a_2=a_1·r^{n-1}=54\cdot {1.1851851851851851}^{2-1}=54\cdot {1.1851851851851851}^1=54\cdot 1.1851851851851851=64$$

$$a_3=a_1·r^{n-1}=54\cdot {1.1851851851851851}^{3-1}=54\cdot {1.1851851851851851}^2=54\cdot 1.4046639231824416=75.85185185185185$$

$$a_4=a_1·r^{n-1}=54\cdot {1.1851851851851851}^{4-1}=54\cdot {1.1851851851851851}^3=54\cdot 1.6647868719199306=89.89849108367625$$

$$a_5=a_1·r^{n-1}=54\cdot {1.1851851851851851}^{5-1}=54\cdot {1.1851851851851851}^4=54\cdot 1.973080737090288=106.54635980287556$$

$$a_6=a_1·r^{n-1}=54\cdot {1.1851851851851851}^{6-1}=54\cdot {1.1851851851851851}^5=54\cdot 2.3384660587736747=126.27716717377844$$

$$a_7=a_1·r^{n-1}=54\cdot {1.1851851851851851}^{7-1}=54\cdot {1.1851851851851851}^6=54\cdot 2.7715153289169474=149.66182776151516$$

$$a_8=a_1·r^{n-1}=54\cdot {1.1851851851851851}^{8-1}=54\cdot {1.1851851851851851}^7=54\cdot 3.284758908346012=177.37698105068463$$

$$a_9=a_1·r^{n-1}=54\cdot {1.1851851851851851}^{9-1}=54\cdot {1.1851851851851851}^8=54\cdot 3.8930475950767542=210.22457013414473$$

$$a_{10}=a_1·r^{n-1}=54\cdot {1.1851851851851851}^{10-1}=54\cdot {1.1851851851851851}^9=54\cdot 4.613982334905783=249.1550460849123$$