সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=75$$ এবং সাধারণ অনুপাত: $$r=0.8$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {0.8}^{2-1}=75\cdot {0.8}^1=75\cdot 0.8=60$$

$$a_3=a_1·r^{n-1}=75\cdot {0.8}^{3-1}=75\cdot {0.8}^2=75\cdot 0.6400000000000001=48.00000000000001$$

$$a_4=a_1·r^{n-1}=75\cdot {0.8}^{4-1}=75\cdot {0.8}^3=75\cdot 0.5120000000000001=38.400000000000006$$

$$a_5=a_1·r^{n-1}=75\cdot {0.8}^{5-1}=75\cdot {0.8}^4=75\cdot 0.4096000000000001=30.720000000000006$$

$$a_6=a_1·r^{n-1}=75\cdot {0.8}^{6-1}=75\cdot {0.8}^5=75\cdot 0.3276800000000001=24.576000000000008$$

$$a_7=a_1·r^{n-1}=75\cdot {0.8}^{7-1}=75\cdot {0.8}^6=75\cdot 0.2621440000000001=19.66080000000001$$

$$a_8=a_1·r^{n-1}=75\cdot {0.8}^{8-1}=75\cdot {0.8}^7=75\cdot 0.20971520000000007=15.728640000000006$$

$$a_9=a_1·r^{n-1}=75\cdot {0.8}^{9-1}=75\cdot {0.8}^8=75\cdot 0.1677721600000001=12.582912000000006$$

$$a_{10}=a_1·r^{n-1}=75\cdot {0.8}^{10-1}=75\cdot {0.8}^9=75\cdot 0.13421772800000006=10.066329600000005$$