সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=416$$ এবং সাধারণ অনুপাত: $$r=0.5625$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=416$$

$$a_2=a_1·r^{n-1}=416\cdot {0.5625}^{2-1}=416\cdot {0.5625}^1=416\cdot 0.5625=234$$

$$a_3=a_1·r^{n-1}=416\cdot {0.5625}^{3-1}=416\cdot {0.5625}^2=416\cdot 0.31640625=131.625$$

$$a_4=a_1·r^{n-1}=416\cdot {0.5625}^{4-1}=416\cdot {0.5625}^3=416\cdot 0.177978515625=74.0390625$$

$$a_5=a_1·r^{n-1}=416\cdot {0.5625}^{5-1}=416\cdot {0.5625}^4=416\cdot 0.1001129150390625=41.64697265625$$

$$a_6=a_1·r^{n-1}=416\cdot {0.5625}^{6-1}=416\cdot {0.5625}^5=416\cdot 0.056313514709472656=23.426422119140625$$

$$a_7=a_1·r^{n-1}=416\cdot {0.5625}^{7-1}=416\cdot {0.5625}^6=416\cdot 0.03167635202407837=13.177362442016602$$

$$a_8=a_1·r^{n-1}=416\cdot {0.5625}^{8-1}=416\cdot {0.5625}^7=416\cdot 0.017817948013544083=7.412266373634338$$

$$a_9=a_1·r^{n-1}=416\cdot {0.5625}^{9-1}=416\cdot {0.5625}^8=416\cdot 0.010022595757618546=4.169399835169315$$

$$a_{10}=a_1·r^{n-1}=416\cdot {0.5625}^{10-1}=416\cdot {0.5625}^9=416\cdot 0.005637710113660432=2.34528740728274$$