সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=165$$ এবং সাধারণ অনুপাত: $$r=0.8$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=165$$

$$a_2=a_1·r^{n-1}=165\cdot {0.8}^{2-1}=165\cdot {0.8}^1=165\cdot 0.8=132$$

$$a_3=a_1·r^{n-1}=165\cdot {0.8}^{3-1}=165\cdot {0.8}^2=165\cdot 0.6400000000000001=105.60000000000002$$

$$a_4=a_1·r^{n-1}=165\cdot {0.8}^{4-1}=165\cdot {0.8}^3=165\cdot 0.5120000000000001=84.48000000000002$$

$$a_5=a_1·r^{n-1}=165\cdot {0.8}^{5-1}=165\cdot {0.8}^4=165\cdot 0.4096000000000001=67.58400000000002$$

$$a_6=a_1·r^{n-1}=165\cdot {0.8}^{6-1}=165\cdot {0.8}^5=165\cdot 0.3276800000000001=54.067200000000014$$

$$a_7=a_1·r^{n-1}=165\cdot {0.8}^{7-1}=165\cdot {0.8}^6=165\cdot 0.2621440000000001=43.253760000000014$$

$$a_8=a_1·r^{n-1}=165\cdot {0.8}^{8-1}=165\cdot {0.8}^7=165\cdot 0.20971520000000007=34.60300800000001$$

$$a_9=a_1·r^{n-1}=165\cdot {0.8}^{9-1}=165\cdot {0.8}^8=165\cdot 0.1677721600000001=27.682406400000016$$

$$a_{10}=a_1·r^{n-1}=165\cdot {0.8}^{10-1}=165\cdot {0.8}^9=165\cdot 0.13421772800000006=22.145925120000012$$