সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=100$$ এবং সাধারণ অনুপাত: $$r=0.49$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=100$$

$$a_2=a_1·r^{n-1}=100\cdot {0.49}^{2-1}=100\cdot {0.49}^1=100\cdot 0.49=49$$

$$a_3=a_1·r^{n-1}=100\cdot {0.49}^{3-1}=100\cdot {0.49}^2=100\cdot 0.24009999999999998=24.009999999999998$$

$$a_4=a_1·r^{n-1}=100\cdot {0.49}^{4-1}=100\cdot {0.49}^3=100\cdot 0.11764899999999999=11.764899999999999$$

$$a_5=a_1·r^{n-1}=100\cdot {0.49}^{5-1}=100\cdot {0.49}^4=100\cdot 0.05764800999999999=5.764800999999999$$

$$a_6=a_1·r^{n-1}=100\cdot {0.49}^{6-1}=100\cdot {0.49}^5=100\cdot 0.028247524899999998=2.82475249$$

$$a_7=a_1·r^{n-1}=100\cdot {0.49}^{7-1}=100\cdot {0.49}^6=100\cdot 0.013841287200999999=1.3841287200999999$$

$$a_8=a_1·r^{n-1}=100\cdot {0.49}^{8-1}=100\cdot {0.49}^7=100\cdot 0.006782230728489999=0.678223072849$$

$$a_9=a_1·r^{n-1}=100\cdot {0.49}^{9-1}=100\cdot {0.49}^8=100\cdot 0.0033232930569600996=0.33232930569600994$$

$$a_{10}=a_1·r^{n-1}=100\cdot {0.49}^{10-1}=100\cdot {0.49}^9=100\cdot 0.0016284135979104488=0.1628413597910449$$