সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=100$$ এবং সাধারণ অনুপাত: $$r=0.88$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=100$$

$$a_2=a_1·r^{n-1}=100\cdot {0.88}^{2-1}=100\cdot {0.88}^1=100\cdot 0.88=88$$

$$a_3=a_1·r^{n-1}=100\cdot {0.88}^{3-1}=100\cdot {0.88}^2=100\cdot 0.7744=77.44$$

$$a_4=a_1·r^{n-1}=100\cdot {0.88}^{4-1}=100\cdot {0.88}^3=100\cdot 0.681472=68.1472$$

$$a_5=a_1·r^{n-1}=100\cdot {0.88}^{5-1}=100\cdot {0.88}^4=100\cdot 0.59969536=59.969536$$

$$a_6=a_1·r^{n-1}=100\cdot {0.88}^{6-1}=100\cdot {0.88}^5=100\cdot 0.5277319168=52.77319168$$

$$a_7=a_1·r^{n-1}=100\cdot {0.88}^{7-1}=100\cdot {0.88}^6=100\cdot 0.464404086784=46.440408678400004$$

$$a_8=a_1·r^{n-1}=100\cdot {0.88}^{8-1}=100\cdot {0.88}^7=100\cdot 0.40867559636992=40.867559636992$$

$$a_9=a_1·r^{n-1}=100\cdot {0.88}^{9-1}=100\cdot {0.88}^8=100\cdot 0.3596345248055296=35.96345248055296$$

$$a_{10}=a_1·r^{n-1}=100\cdot {0.88}^{10-1}=100\cdot {0.88}^9=100\cdot 0.31647838182886606=31.647838182886606$$