সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=80$$ এবং সাধারণ অনুপাত: $$r=0.7$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=80$$

$$a_2=a_1·r^{n-1}=80\cdot {0.7}^{2-1}=80\cdot {0.7}^1=80\cdot 0.7=56$$

$$a_3=a_1·r^{n-1}=80\cdot {0.7}^{3-1}=80\cdot {0.7}^2=80\cdot 0.48999999999999994=39.199999999999996$$

$$a_4=a_1·r^{n-1}=80\cdot {0.7}^{4-1}=80\cdot {0.7}^3=80\cdot 0.3429999999999999=27.439999999999994$$

$$a_5=a_1·r^{n-1}=80\cdot {0.7}^{5-1}=80\cdot {0.7}^4=80\cdot 0.24009999999999995=19.207999999999995$$

$$a_6=a_1·r^{n-1}=80\cdot {0.7}^{6-1}=80\cdot {0.7}^5=80\cdot 0.16806999999999994=13.445599999999995$$

$$a_7=a_1·r^{n-1}=80\cdot {0.7}^{7-1}=80\cdot {0.7}^6=80\cdot 0.11764899999999996=9.411919999999997$$

$$a_8=a_1·r^{n-1}=80\cdot {0.7}^{8-1}=80\cdot {0.7}^7=80\cdot 0.08235429999999996=6.5883439999999975$$

$$a_9=a_1·r^{n-1}=80\cdot {0.7}^{9-1}=80\cdot {0.7}^8=80\cdot 0.05764800999999997=4.611840799999998$$

$$a_{10}=a_1·r^{n-1}=80\cdot {0.7}^{10-1}=80\cdot {0.7}^9=80\cdot 0.04035360699999998=3.2282885599999984$$