పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=45$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.4444444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=45$$

$$a_2=a_1·r^{n-1}=45\cdot {0.4444444444444444}^{2-1}=45\cdot {0.4444444444444444}^1=45\cdot 0.4444444444444444=20$$

$$a_3=a_1·r^{n-1}=45\cdot {0.4444444444444444}^{3-1}=45\cdot {0.4444444444444444}^2=45\cdot 0.19753086419753085=8.88888888888889$$

$$a_4=a_1·r^{n-1}=45\cdot {0.4444444444444444}^{4-1}=45\cdot {0.4444444444444444}^3=45\cdot 0.08779149519890259=3.950617283950616$$

$$a_5=a_1·r^{n-1}=45\cdot {0.4444444444444444}^{5-1}=45\cdot {0.4444444444444444}^4=45\cdot 0.039018442310623375=1.7558299039780518$$

$$a_6=a_1·r^{n-1}=45\cdot {0.4444444444444444}^{6-1}=45\cdot {0.4444444444444444}^5=45\cdot 0.01734152991583261=0.7803688462124674$$

$$a_7=a_1·r^{n-1}=45\cdot {0.4444444444444444}^{7-1}=45\cdot {0.4444444444444444}^6=45\cdot 0.007707346629258937=0.34683059831665214$$

$$a_8=a_1·r^{n-1}=45\cdot {0.4444444444444444}^{8-1}=45\cdot {0.4444444444444444}^7=45\cdot 0.0034254873907817495=0.15414693258517873$$

$$a_9=a_1·r^{n-1}=45\cdot {0.4444444444444444}^{9-1}=45\cdot {0.4444444444444444}^8=45\cdot 0.001522438840347444=0.06850974781563499$$

$$a_{10}=a_1·r^{n-1}=45\cdot {0.4444444444444444}^{10-1}=45\cdot {0.4444444444444444}^9=45\cdot 0.000676639484598864=0.03044877680694888$$