పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=360$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.4444444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=360$$

$$a_2=a_1·r^{n-1}=360\cdot {0.4444444444444444}^{2-1}=360\cdot {0.4444444444444444}^1=360\cdot 0.4444444444444444=160$$

$$a_3=a_1·r^{n-1}=360\cdot {0.4444444444444444}^{3-1}=360\cdot {0.4444444444444444}^2=360\cdot 0.19753086419753085=71.11111111111111$$

$$a_4=a_1·r^{n-1}=360\cdot {0.4444444444444444}^{4-1}=360\cdot {0.4444444444444444}^3=360\cdot 0.08779149519890259=31.60493827160493$$

$$a_5=a_1·r^{n-1}=360\cdot {0.4444444444444444}^{5-1}=360\cdot {0.4444444444444444}^4=360\cdot 0.039018442310623375=14.046639231824415$$

$$a_6=a_1·r^{n-1}=360\cdot {0.4444444444444444}^{6-1}=360\cdot {0.4444444444444444}^5=360\cdot 0.01734152991583261=6.242950769699739$$

$$a_7=a_1·r^{n-1}=360\cdot {0.4444444444444444}^{7-1}=360\cdot {0.4444444444444444}^6=360\cdot 0.007707346629258937=2.774644786533217$$

$$a_8=a_1·r^{n-1}=360\cdot {0.4444444444444444}^{8-1}=360\cdot {0.4444444444444444}^7=360\cdot 0.0034254873907817495=1.2331754606814298$$

$$a_9=a_1·r^{n-1}=360\cdot {0.4444444444444444}^{9-1}=360\cdot {0.4444444444444444}^8=360\cdot 0.001522438840347444=0.5480779825250799$$

$$a_{10}=a_1·r^{n-1}=360\cdot {0.4444444444444444}^{10-1}=360\cdot {0.4444444444444444}^9=360\cdot 0.000676639484598864=0.24359021445559104$$