সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=75$$ এবং সাধারণ অনুপাত: $$r=0.16$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {0.16}^{2-1}=75\cdot {0.16}^1=75\cdot 0.16=12$$

$$a_3=a_1·r^{n-1}=75\cdot {0.16}^{3-1}=75\cdot {0.16}^2=75\cdot 0.0256=1.9200000000000002$$

$$a_4=a_1·r^{n-1}=75\cdot {0.16}^{4-1}=75\cdot {0.16}^3=75\cdot 0.004096000000000001=0.30720000000000003$$

$$a_5=a_1·r^{n-1}=75\cdot {0.16}^{5-1}=75\cdot {0.16}^4=75\cdot 0.00065536=0.049152$$

$$a_6=a_1·r^{n-1}=75\cdot {0.16}^{6-1}=75\cdot {0.16}^5=75\cdot 0.00010485760000000002=0.007864320000000001$$

$$a_7=a_1·r^{n-1}=75\cdot {0.16}^{7-1}=75\cdot {0.16}^6=75\cdot 1.6777216000000003E-05=0.0012582912000000002$$

$$a_8=a_1·r^{n-1}=75\cdot {0.16}^{8-1}=75\cdot {0.16}^7=75\cdot 2.6843545600000004E-06=0.00020132659200000004$$

$$a_9=a_1·r^{n-1}=75\cdot {0.16}^{9-1}=75\cdot {0.16}^8=75\cdot 4.294967296000001E-07=3.2212254720000005E-05$$

$$a_{10}=a_1·r^{n-1}=75\cdot {0.16}^{10-1}=75\cdot {0.16}^9=75\cdot 6.871947673600002E-08=5.153960755200002E-06$$