সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=420$$ এবং সাধারণ অনুপাত: $$r=0.7$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=420$$

$$a_2=a_1·r^{n-1}=420\cdot {0.7}^{2-1}=420\cdot {0.7}^1=420\cdot 0.7=294$$

$$a_3=a_1·r^{n-1}=420\cdot {0.7}^{3-1}=420\cdot {0.7}^2=420\cdot 0.48999999999999994=205.79999999999998$$

$$a_4=a_1·r^{n-1}=420\cdot {0.7}^{4-1}=420\cdot {0.7}^3=420\cdot 0.3429999999999999=144.05999999999997$$

$$a_5=a_1·r^{n-1}=420\cdot {0.7}^{5-1}=420\cdot {0.7}^4=420\cdot 0.24009999999999995=100.84199999999998$$

$$a_6=a_1·r^{n-1}=420\cdot {0.7}^{6-1}=420\cdot {0.7}^5=420\cdot 0.16806999999999994=70.58939999999997$$

$$a_7=a_1·r^{n-1}=420\cdot {0.7}^{7-1}=420\cdot {0.7}^6=420\cdot 0.11764899999999996=49.412579999999984$$

$$a_8=a_1·r^{n-1}=420\cdot {0.7}^{8-1}=420\cdot {0.7}^7=420\cdot 0.08235429999999996=34.588805999999984$$

$$a_9=a_1·r^{n-1}=420\cdot {0.7}^{9-1}=420\cdot {0.7}^8=420\cdot 0.05764800999999997=24.21216419999999$$

$$a_{10}=a_1·r^{n-1}=420\cdot {0.7}^{10-1}=420\cdot {0.7}^9=420\cdot 0.04035360699999998=16.948514939999992$$