সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=90$$ এবং সাধারণ অনুপাত: $$r=0.4$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=90$$

$$a_2=a_1·r^{n-1}=90\cdot {0.4}^{2-1}=90\cdot {0.4}^1=90\cdot 0.4=36$$

$$a_3=a_1·r^{n-1}=90\cdot {0.4}^{3-1}=90\cdot {0.4}^2=90\cdot 0.16000000000000003=14.400000000000002$$

$$a_4=a_1·r^{n-1}=90\cdot {0.4}^{4-1}=90\cdot {0.4}^3=90\cdot 0.06400000000000002=5.760000000000002$$

$$a_5=a_1·r^{n-1}=90\cdot {0.4}^{5-1}=90\cdot {0.4}^4=90\cdot 0.025600000000000005=2.3040000000000003$$

$$a_6=a_1·r^{n-1}=90\cdot {0.4}^{6-1}=90\cdot {0.4}^5=90\cdot 0.010240000000000003=0.9216000000000002$$

$$a_7=a_1·r^{n-1}=90\cdot {0.4}^{7-1}=90\cdot {0.4}^6=90\cdot 0.0040960000000000015=0.36864000000000013$$

$$a_8=a_1·r^{n-1}=90\cdot {0.4}^{8-1}=90\cdot {0.4}^7=90\cdot 0.0016384000000000006=0.14745600000000006$$

$$a_9=a_1·r^{n-1}=90\cdot {0.4}^{9-1}=90\cdot {0.4}^8=90\cdot 0.0006553600000000003=0.05898240000000003$$

$$a_{10}=a_1·r^{n-1}=90\cdot {0.4}^{10-1}=90\cdot {0.4}^9=90\cdot 0.0002621440000000001=0.02359296000000001$$