সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=75$$ এবং সাধারণ অনুপাত: $$r=0.36$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {0.36}^{2-1}=75\cdot {0.36}^1=75\cdot 0.36=27$$

$$a_3=a_1·r^{n-1}=75\cdot {0.36}^{3-1}=75\cdot {0.36}^2=75\cdot 0.1296=9.719999999999999$$

$$a_4=a_1·r^{n-1}=75\cdot {0.36}^{4-1}=75\cdot {0.36}^3=75\cdot 0.046655999999999996=3.4991999999999996$$

$$a_5=a_1·r^{n-1}=75\cdot {0.36}^{5-1}=75\cdot {0.36}^4=75\cdot 0.016796159999999997=1.2597119999999997$$

$$a_6=a_1·r^{n-1}=75\cdot {0.36}^{6-1}=75\cdot {0.36}^5=75\cdot 0.006046617599999999=0.45349631999999995$$

$$a_7=a_1·r^{n-1}=75\cdot {0.36}^{7-1}=75\cdot {0.36}^6=75\cdot 0.0021767823359999995=0.16325867519999995$$

$$a_8=a_1·r^{n-1}=75\cdot {0.36}^{8-1}=75\cdot {0.36}^7=75\cdot 0.0007836416409599998=0.058773123071999986$$

$$a_9=a_1·r^{n-1}=75\cdot {0.36}^{9-1}=75\cdot {0.36}^8=75\cdot 0.0002821109907455999=0.021158324305919993$$

$$a_{10}=a_1·r^{n-1}=75\cdot {0.36}^{10-1}=75\cdot {0.36}^9=75\cdot 0.00010155995666841596=0.007616996750131197$$