সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=75$$ এবং সাধারণ অনুপাত: $$r=-0.2$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot -{0.2}^{2-1}=75\cdot -{0.2}^1=75\cdot -0.2=-15$$

$$a_3=a_1·r^{n-1}=75\cdot -{0.2}^{3-1}=75\cdot -{0.2}^2=75\cdot 0.04000000000000001=3.0000000000000004$$

$$a_4=a_1·r^{n-1}=75\cdot -{0.2}^{4-1}=75\cdot -{0.2}^3=75\cdot -0.008000000000000002=-0.6000000000000001$$

$$a_5=a_1·r^{n-1}=75\cdot -{0.2}^{5-1}=75\cdot -{0.2}^4=75\cdot 0.0016000000000000003=0.12000000000000002$$

$$a_6=a_1·r^{n-1}=75\cdot -{0.2}^{6-1}=75\cdot -{0.2}^5=75\cdot -0.0003200000000000001=-0.024000000000000007$$

$$a_7=a_1·r^{n-1}=75\cdot -{0.2}^{7-1}=75\cdot -{0.2}^6=75\cdot 6.400000000000002E-05=0.004800000000000002$$

$$a_8=a_1·r^{n-1}=75\cdot -{0.2}^{8-1}=75\cdot -{0.2}^7=75\cdot -1.2800000000000005E-05=-0.0009600000000000003$$

$$a_9=a_1·r^{n-1}=75\cdot -{0.2}^{9-1}=75\cdot -{0.2}^8=75\cdot 2.5600000000000013E-06=0.00019200000000000009$$

$$a_{10}=a_1·r^{n-1}=75\cdot -{0.2}^{10-1}=75\cdot -{0.2}^9=75\cdot -5.120000000000002E-07=-3.840000000000002E-05$$