పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=144$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.6944444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=144$$

$$a_2=a_1·r^{n-1}=144\cdot {0.6944444444444444}^{2-1}=144\cdot {0.6944444444444444}^1=144\cdot 0.6944444444444444=100$$

$$a_3=a_1·r^{n-1}=144\cdot {0.6944444444444444}^{3-1}=144\cdot {0.6944444444444444}^2=144\cdot 0.48225308641975306=69.44444444444444$$

$$a_4=a_1·r^{n-1}=144\cdot {0.6944444444444444}^{4-1}=144\cdot {0.6944444444444444}^3=144\cdot 0.33489797668038407=48.2253086419753$$

$$a_5=a_1·r^{n-1}=144\cdot {0.6944444444444444}^{5-1}=144\cdot {0.6944444444444444}^4=144\cdot 0.2325680393613778=33.4897976680384$$

$$a_6=a_1·r^{n-1}=144\cdot {0.6944444444444444}^{6-1}=144\cdot {0.6944444444444444}^5=144\cdot 0.1615055828898457=23.256803936137782$$

$$a_7=a_1·r^{n-1}=144\cdot {0.6944444444444444}^{7-1}=144\cdot {0.6944444444444444}^6=144\cdot 0.11215665478461506=16.15055828898457$$

$$a_8=a_1·r^{n-1}=144\cdot {0.6944444444444444}^{8-1}=144\cdot {0.6944444444444444}^7=144\cdot 0.07788656582264934=11.215665478461505$$

$$a_9=a_1·r^{n-1}=144\cdot {0.6944444444444444}^{9-1}=144\cdot {0.6944444444444444}^8=144\cdot 0.054087892932395375=7.788656582264934$$

$$a_{10}=a_1·r^{n-1}=144\cdot {0.6944444444444444}^{10-1}=144\cdot {0.6944444444444444}^9=144\cdot 0.0375610367586079=5.408789293239537$$