সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=30$$ এবং সাধারণ অনুপাত: $$r=0.4$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=30$$

$$a_2=a_1·r^{n-1}=30\cdot {0.4}^{2-1}=30\cdot {0.4}^1=30\cdot 0.4=12$$

$$a_3=a_1·r^{n-1}=30\cdot {0.4}^{3-1}=30\cdot {0.4}^2=30\cdot 0.16000000000000003=4.800000000000001$$

$$a_4=a_1·r^{n-1}=30\cdot {0.4}^{4-1}=30\cdot {0.4}^3=30\cdot 0.06400000000000002=1.9200000000000004$$

$$a_5=a_1·r^{n-1}=30\cdot {0.4}^{5-1}=30\cdot {0.4}^4=30\cdot 0.025600000000000005=0.7680000000000001$$

$$a_6=a_1·r^{n-1}=30\cdot {0.4}^{6-1}=30\cdot {0.4}^5=30\cdot 0.010240000000000003=0.3072000000000001$$

$$a_7=a_1·r^{n-1}=30\cdot {0.4}^{7-1}=30\cdot {0.4}^6=30\cdot 0.0040960000000000015=0.12288000000000004$$

$$a_8=a_1·r^{n-1}=30\cdot {0.4}^{8-1}=30\cdot {0.4}^7=30\cdot 0.0016384000000000006=0.049152000000000015$$

$$a_9=a_1·r^{n-1}=30\cdot {0.4}^{9-1}=30\cdot {0.4}^8=30\cdot 0.0006553600000000003=0.01966080000000001$$

$$a_{10}=a_1·r^{n-1}=30\cdot {0.4}^{10-1}=30\cdot {0.4}^9=30\cdot 0.0002621440000000001=0.007864320000000005$$