పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=66$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.12121212121212122$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=66$$

$$a_2=a_1·r^{n-1}=66\cdot {0.12121212121212122}^{2-1}=66\cdot {0.12121212121212122}^1=66\cdot 0.12121212121212122=8$$

$$a_3=a_1·r^{n-1}=66\cdot {0.12121212121212122}^{3-1}=66\cdot {0.12121212121212122}^2=66\cdot 0.014692378328741967=0.9696969696969698$$

$$a_4=a_1·r^{n-1}=66\cdot {0.12121212121212122}^{4-1}=66\cdot {0.12121212121212122}^3=66\cdot 0.0017808943428778141=0.11753902662993573$$

$$a_5=a_1·r^{n-1}=66\cdot {0.12121212121212122}^{5-1}=66\cdot {0.12121212121212122}^4=66\cdot 0.00021586598095488656=0.014247154743022513$$

$$a_6=a_1·r^{n-1}=66\cdot {0.12121212121212122}^{6-1}=66\cdot {0.12121212121212122}^5=66\cdot 2.616557344907716E-05=0.0017269278476390924$$

$$a_7=a_1·r^{n-1}=66\cdot {0.12121212121212122}^{7-1}=66\cdot {0.12121212121212122}^6=66\cdot 3.1715846604942015E-06=0.0002093245875926173$$

$$a_8=a_1·r^{n-1}=66\cdot {0.12121212121212122}^{8-1}=66\cdot {0.12121212121212122}^7=66\cdot 3.8443450430232743E-07=2.5372677283953612E-05$$

$$a_9=a_1·r^{n-1}=66\cdot {0.12121212121212122}^{9-1}=66\cdot {0.12121212121212122}^8=66\cdot 4.659812173361545E-08=3.0754760344186195E-06$$

$$a_{10}=a_1·r^{n-1}=66\cdot {0.12121212121212122}^{10-1}=66\cdot {0.12121212121212122}^9=66\cdot 5.648257179832176E-09=3.727849738689236E-07$$