పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=108$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.6944444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=108$$

$$a_2=a_1·r^{n-1}=108\cdot {0.6944444444444444}^{2-1}=108\cdot {0.6944444444444444}^1=108\cdot 0.6944444444444444=75$$

$$a_3=a_1·r^{n-1}=108\cdot {0.6944444444444444}^{3-1}=108\cdot {0.6944444444444444}^2=108\cdot 0.48225308641975306=52.08333333333333$$

$$a_4=a_1·r^{n-1}=108\cdot {0.6944444444444444}^{4-1}=108\cdot {0.6944444444444444}^3=108\cdot 0.33489797668038407=36.16898148148148$$

$$a_5=a_1·r^{n-1}=108\cdot {0.6944444444444444}^{5-1}=108\cdot {0.6944444444444444}^4=108\cdot 0.2325680393613778=25.1173482510288$$

$$a_6=a_1·r^{n-1}=108\cdot {0.6944444444444444}^{6-1}=108\cdot {0.6944444444444444}^5=108\cdot 0.1615055828898457=17.442602952103336$$

$$a_7=a_1·r^{n-1}=108\cdot {0.6944444444444444}^{7-1}=108\cdot {0.6944444444444444}^6=108\cdot 0.11215665478461506=12.112918716738427$$

$$a_8=a_1·r^{n-1}=108\cdot {0.6944444444444444}^{8-1}=108\cdot {0.6944444444444444}^7=108\cdot 0.07788656582264934=8.411749108846129$$

$$a_9=a_1·r^{n-1}=108\cdot {0.6944444444444444}^{9-1}=108\cdot {0.6944444444444444}^8=108\cdot 0.054087892932395375=5.841492436698701$$

$$a_{10}=a_1·r^{n-1}=108\cdot {0.6944444444444444}^{10-1}=108\cdot {0.6944444444444444}^9=108\cdot 0.0375610367586079=4.056591969929653$$