সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=1,176$$ এবং সাধারণ অনুপাত: $$r=0.5$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=1176$$

$$a_2=a_1·r^{n-1}=1176\cdot {0.5}^{2-1}=1176\cdot {0.5}^1=1176\cdot 0.5=588$$

$$a_3=a_1·r^{n-1}=1176\cdot {0.5}^{3-1}=1176\cdot {0.5}^2=1176\cdot 0.25=294$$

$$a_4=a_1·r^{n-1}=1176\cdot {0.5}^{4-1}=1176\cdot {0.5}^3=1176\cdot 0.125=147$$

$$a_5=a_1·r^{n-1}=1176\cdot {0.5}^{5-1}=1176\cdot {0.5}^4=1176\cdot 0.0625=73.5$$

$$a_6=a_1·r^{n-1}=1176\cdot {0.5}^{6-1}=1176\cdot {0.5}^5=1176\cdot 0.03125=36.75$$

$$a_7=a_1·r^{n-1}=1176\cdot {0.5}^{7-1}=1176\cdot {0.5}^6=1176\cdot 0.015625=18.375$$

$$a_8=a_1·r^{n-1}=1176\cdot {0.5}^{8-1}=1176\cdot {0.5}^7=1176\cdot 0.0078125=9.1875$$

$$a_9=a_1·r^{n-1}=1176\cdot {0.5}^{9-1}=1176\cdot {0.5}^8=1176\cdot 0.00390625=4.59375$$

$$a_{10}=a_1·r^{n-1}=1176\cdot {0.5}^{10-1}=1176\cdot {0.5}^9=1176\cdot 0.001953125=2.296875$$