పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=72$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.6944444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=72$$

$$a_2=a_1·r^{n-1}=72\cdot {0.6944444444444444}^{2-1}=72\cdot {0.6944444444444444}^1=72\cdot 0.6944444444444444=50$$

$$a_3=a_1·r^{n-1}=72\cdot {0.6944444444444444}^{3-1}=72\cdot {0.6944444444444444}^2=72\cdot 0.48225308641975306=34.72222222222222$$

$$a_4=a_1·r^{n-1}=72\cdot {0.6944444444444444}^{4-1}=72\cdot {0.6944444444444444}^3=72\cdot 0.33489797668038407=24.11265432098765$$

$$a_5=a_1·r^{n-1}=72\cdot {0.6944444444444444}^{5-1}=72\cdot {0.6944444444444444}^4=72\cdot 0.2325680393613778=16.7448988340192$$

$$a_6=a_1·r^{n-1}=72\cdot {0.6944444444444444}^{6-1}=72\cdot {0.6944444444444444}^5=72\cdot 0.1615055828898457=11.628401968068891$$

$$a_7=a_1·r^{n-1}=72\cdot {0.6944444444444444}^{7-1}=72\cdot {0.6944444444444444}^6=72\cdot 0.11215665478461506=8.075279144492285$$

$$a_8=a_1·r^{n-1}=72\cdot {0.6944444444444444}^{8-1}=72\cdot {0.6944444444444444}^7=72\cdot 0.07788656582264934=5.607832739230752$$

$$a_9=a_1·r^{n-1}=72\cdot {0.6944444444444444}^{9-1}=72\cdot {0.6944444444444444}^8=72\cdot 0.054087892932395375=3.894328291132467$$

$$a_{10}=a_1·r^{n-1}=72\cdot {0.6944444444444444}^{10-1}=72\cdot {0.6944444444444444}^9=72\cdot 0.0375610367586079=2.7043946466197686$$