పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=27$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.4444444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=27$$

$$a_2=a_1·r^{n-1}=27\cdot {0.4444444444444444}^{2-1}=27\cdot {0.4444444444444444}^1=27\cdot 0.4444444444444444=12$$

$$a_3=a_1·r^{n-1}=27\cdot {0.4444444444444444}^{3-1}=27\cdot {0.4444444444444444}^2=27\cdot 0.19753086419753085=5.333333333333333$$

$$a_4=a_1·r^{n-1}=27\cdot {0.4444444444444444}^{4-1}=27\cdot {0.4444444444444444}^3=27\cdot 0.08779149519890259=2.37037037037037$$

$$a_5=a_1·r^{n-1}=27\cdot {0.4444444444444444}^{5-1}=27\cdot {0.4444444444444444}^4=27\cdot 0.039018442310623375=1.0534979423868311$$

$$a_6=a_1·r^{n-1}=27\cdot {0.4444444444444444}^{6-1}=27\cdot {0.4444444444444444}^5=27\cdot 0.01734152991583261=0.46822130772748044$$

$$a_7=a_1·r^{n-1}=27\cdot {0.4444444444444444}^{7-1}=27\cdot {0.4444444444444444}^6=27\cdot 0.007707346629258937=0.2080983589899913$$

$$a_8=a_1·r^{n-1}=27\cdot {0.4444444444444444}^{8-1}=27\cdot {0.4444444444444444}^7=27\cdot 0.0034254873907817495=0.09248815955110723$$

$$a_9=a_1·r^{n-1}=27\cdot {0.4444444444444444}^{9-1}=27\cdot {0.4444444444444444}^8=27\cdot 0.001522438840347444=0.04110584868938099$$

$$a_{10}=a_1·r^{n-1}=27\cdot {0.4444444444444444}^{10-1}=27\cdot {0.4444444444444444}^9=27\cdot 0.000676639484598864=0.018269266084169327$$