పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=216$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.6944444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=216$$

$$a_2=a_1·r^{n-1}=216\cdot {0.6944444444444444}^{2-1}=216\cdot {0.6944444444444444}^1=216\cdot 0.6944444444444444=150$$

$$a_3=a_1·r^{n-1}=216\cdot {0.6944444444444444}^{3-1}=216\cdot {0.6944444444444444}^2=216\cdot 0.48225308641975306=104.16666666666666$$

$$a_4=a_1·r^{n-1}=216\cdot {0.6944444444444444}^{4-1}=216\cdot {0.6944444444444444}^3=216\cdot 0.33489797668038407=72.33796296296296$$

$$a_5=a_1·r^{n-1}=216\cdot {0.6944444444444444}^{5-1}=216\cdot {0.6944444444444444}^4=216\cdot 0.2325680393613778=50.2346965020576$$

$$a_6=a_1·r^{n-1}=216\cdot {0.6944444444444444}^{6-1}=216\cdot {0.6944444444444444}^5=216\cdot 0.1615055828898457=34.88520590420667$$

$$a_7=a_1·r^{n-1}=216\cdot {0.6944444444444444}^{7-1}=216\cdot {0.6944444444444444}^6=216\cdot 0.11215665478461506=24.225837433476855$$

$$a_8=a_1·r^{n-1}=216\cdot {0.6944444444444444}^{8-1}=216\cdot {0.6944444444444444}^7=216\cdot 0.07788656582264934=16.823498217692258$$

$$a_9=a_1·r^{n-1}=216\cdot {0.6944444444444444}^{9-1}=216\cdot {0.6944444444444444}^8=216\cdot 0.054087892932395375=11.682984873397402$$

$$a_{10}=a_1·r^{n-1}=216\cdot {0.6944444444444444}^{10-1}=216\cdot {0.6944444444444444}^9=216\cdot 0.0375610367586079=8.113183939859306$$