সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=100$$ এবং সাধারণ অনুপাত: $$r=0.7$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=100$$

$$a_2=a_1·r^{n-1}=100\cdot {0.7}^{2-1}=100\cdot {0.7}^1=100\cdot 0.7=70$$

$$a_3=a_1·r^{n-1}=100\cdot {0.7}^{3-1}=100\cdot {0.7}^2=100\cdot 0.48999999999999994=48.99999999999999$$

$$a_4=a_1·r^{n-1}=100\cdot {0.7}^{4-1}=100\cdot {0.7}^3=100\cdot 0.3429999999999999=34.29999999999999$$

$$a_5=a_1·r^{n-1}=100\cdot {0.7}^{5-1}=100\cdot {0.7}^4=100\cdot 0.24009999999999995=24.009999999999994$$

$$a_6=a_1·r^{n-1}=100\cdot {0.7}^{6-1}=100\cdot {0.7}^5=100\cdot 0.16806999999999994=16.806999999999995$$

$$a_7=a_1·r^{n-1}=100\cdot {0.7}^{7-1}=100\cdot {0.7}^6=100\cdot 0.11764899999999996=11.764899999999995$$

$$a_8=a_1·r^{n-1}=100\cdot {0.7}^{8-1}=100\cdot {0.7}^7=100\cdot 0.08235429999999996=8.235429999999996$$

$$a_9=a_1·r^{n-1}=100\cdot {0.7}^{9-1}=100\cdot {0.7}^8=100\cdot 0.05764800999999997=5.764800999999997$$

$$a_{10}=a_1·r^{n-1}=100\cdot {0.7}^{10-1}=100\cdot {0.7}^9=100\cdot 0.04035360699999998=4.035360699999998$$