সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=65$$ এবং সাধারণ অনুপাত: $$r=0.7384615384615385$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=65$$

$$a_2=a_1·r^{n-1}=65\cdot {0.7384615384615385}^{2-1}=65\cdot {0.7384615384615385}^1=65\cdot 0.7384615384615385=48$$

$$a_3=a_1·r^{n-1}=65\cdot {0.7384615384615385}^{3-1}=65\cdot {0.7384615384615385}^2=65\cdot 0.5453254437869823=35.44615384615385$$

$$a_4=a_1·r^{n-1}=65\cdot {0.7384615384615385}^{4-1}=65\cdot {0.7384615384615385}^3=65\cdot 0.40270186618115617=26.175621301775152$$

$$a_5=a_1·r^{n-1}=65\cdot {0.7384615384615385}^{5-1}=65\cdot {0.7384615384615385}^4=65\cdot 0.2973798396414692=19.329689576695497$$

$$a_6=a_1·r^{n-1}=65\cdot {0.7384615384615385}^{6-1}=65\cdot {0.7384615384615385}^5=65\cdot 0.21960357388908497=14.274232302790523$$

$$a_7=a_1·r^{n-1}=65\cdot {0.7384615384615385}^{7-1}=65\cdot {0.7384615384615385}^6=65\cdot 0.16216879302578582=10.54097154667608$$

$$a_8=a_1·r^{n-1}=65\cdot {0.7384615384615385}^{8-1}=65\cdot {0.7384615384615385}^7=65\cdot 0.11975541638827261=7.78410206523772$$

$$a_9=a_1·r^{n-1}=65\cdot {0.7384615384615385}^{9-1}=65\cdot {0.7384615384615385}^8=65\cdot 0.08843476902518593=5.748259986637086$$

$$a_{10}=a_1·r^{n-1}=65\cdot {0.7384615384615385}^{10-1}=65\cdot {0.7384615384615385}^9=65\cdot 0.06530567558782963=4.244868913208926$$