সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=60$$ এবং সাধারণ অনুপাত: $$r=0.65$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=60$$

$$a_2=a_1·r^{n-1}=60\cdot {0.65}^{2-1}=60\cdot {0.65}^1=60\cdot 0.65=39$$

$$a_3=a_1·r^{n-1}=60\cdot {0.65}^{3-1}=60\cdot {0.65}^2=60\cdot 0.42250000000000004=25.35$$

$$a_4=a_1·r^{n-1}=60\cdot {0.65}^{4-1}=60\cdot {0.65}^3=60\cdot 0.274625=16.4775$$

$$a_5=a_1·r^{n-1}=60\cdot {0.65}^{5-1}=60\cdot {0.65}^4=60\cdot 0.17850625000000003=10.710375000000003$$

$$a_6=a_1·r^{n-1}=60\cdot {0.65}^{6-1}=60\cdot {0.65}^5=60\cdot 0.11602906250000002=6.961743750000001$$

$$a_7=a_1·r^{n-1}=60\cdot {0.65}^{7-1}=60\cdot {0.65}^6=60\cdot 0.07541889062500001=4.525133437500001$$

$$a_8=a_1·r^{n-1}=60\cdot {0.65}^{8-1}=60\cdot {0.65}^7=60\cdot 0.049022278906250015=2.941336734375001$$

$$a_9=a_1·r^{n-1}=60\cdot {0.65}^{9-1}=60\cdot {0.65}^8=60\cdot 0.03186448128906251=1.9118688773437507$$

$$a_{10}=a_1·r^{n-1}=60\cdot {0.65}^{10-1}=60\cdot {0.65}^9=60\cdot 0.02071191283789063=1.2427147702734378$$