పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=90$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.4444444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=90$$

$$a_2=a_1·r^{n-1}=90\cdot {0.4444444444444444}^{2-1}=90\cdot {0.4444444444444444}^1=90\cdot 0.4444444444444444=40$$

$$a_3=a_1·r^{n-1}=90\cdot {0.4444444444444444}^{3-1}=90\cdot {0.4444444444444444}^2=90\cdot 0.19753086419753085=17.77777777777778$$

$$a_4=a_1·r^{n-1}=90\cdot {0.4444444444444444}^{4-1}=90\cdot {0.4444444444444444}^3=90\cdot 0.08779149519890259=7.901234567901232$$

$$a_5=a_1·r^{n-1}=90\cdot {0.4444444444444444}^{5-1}=90\cdot {0.4444444444444444}^4=90\cdot 0.039018442310623375=3.5116598079561037$$

$$a_6=a_1·r^{n-1}=90\cdot {0.4444444444444444}^{6-1}=90\cdot {0.4444444444444444}^5=90\cdot 0.01734152991583261=1.5607376924249348$$

$$a_7=a_1·r^{n-1}=90\cdot {0.4444444444444444}^{7-1}=90\cdot {0.4444444444444444}^6=90\cdot 0.007707346629258937=0.6936611966333043$$

$$a_8=a_1·r^{n-1}=90\cdot {0.4444444444444444}^{8-1}=90\cdot {0.4444444444444444}^7=90\cdot 0.0034254873907817495=0.30829386517035745$$

$$a_9=a_1·r^{n-1}=90\cdot {0.4444444444444444}^{9-1}=90\cdot {0.4444444444444444}^8=90\cdot 0.001522438840347444=0.13701949563126997$$

$$a_{10}=a_1·r^{n-1}=90\cdot {0.4444444444444444}^{10-1}=90\cdot {0.4444444444444444}^9=90\cdot 0.000676639484598864=0.06089755361389776$$