সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=64$$ এবং সাধারণ অনুপাত: $$r=1.40625$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=64$$

$$a_2=a_1·r^{n-1}=64\cdot {1.40625}^{2-1}=64\cdot {1.40625}^1=64\cdot 1.40625=90$$

$$a_3=a_1·r^{n-1}=64\cdot {1.40625}^{3-1}=64\cdot {1.40625}^2=64\cdot 1.9775390625=126.5625$$

$$a_4=a_1·r^{n-1}=64\cdot {1.40625}^{4-1}=64\cdot {1.40625}^3=64\cdot 2.780914306640625=177.978515625$$

$$a_5=a_1·r^{n-1}=64\cdot {1.40625}^{5-1}=64\cdot {1.40625}^4=64\cdot 3.910660743713379=250.28228759765625$$

$$a_6=a_1·r^{n-1}=64\cdot {1.40625}^{6-1}=64\cdot {1.40625}^5=64\cdot 5.499366670846939=351.9594669342041$$

$$a_7=a_1·r^{n-1}=64\cdot {1.40625}^{7-1}=64\cdot {1.40625}^6=64\cdot 7.733484380878508=494.9430003762245$$

$$a_8=a_1·r^{n-1}=64\cdot {1.40625}^{8-1}=64\cdot {1.40625}^7=64\cdot 10.875212410610402=696.0135942790657$$

$$a_9=a_1·r^{n-1}=64\cdot {1.40625}^{9-1}=64\cdot {1.40625}^8=64\cdot 15.293267452420878=978.7691169549362$$

$$a_{10}=a_1·r^{n-1}=64\cdot {1.40625}^{10-1}=64\cdot {1.40625}^9=64\cdot 21.50615735496686=1376.394070717879$$