పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=90$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.5444444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=90$$

$$a_2=a_1·r^{n-1}=90\cdot {0.5444444444444444}^{2-1}=90\cdot {0.5444444444444444}^1=90\cdot 0.5444444444444444=48.99999999999999$$

$$a_3=a_1·r^{n-1}=90\cdot {0.5444444444444444}^{3-1}=90\cdot {0.5444444444444444}^2=90\cdot 0.2964197530864197=26.677777777777774$$

$$a_4=a_1·r^{n-1}=90\cdot {0.5444444444444444}^{4-1}=90\cdot {0.5444444444444444}^3=90\cdot 0.16138408779149516=14.524567901234564$$

$$a_5=a_1·r^{n-1}=90\cdot {0.5444444444444444}^{5-1}=90\cdot {0.5444444444444444}^4=90\cdot 0.08786467001981402=7.907820301783262$$

$$a_6=a_1·r^{n-1}=90\cdot {0.5444444444444444}^{6-1}=90\cdot {0.5444444444444444}^5=90\cdot 0.047837431455232074=4.305368830970886$$

$$a_7=a_1·r^{n-1}=90\cdot {0.5444444444444444}^{7-1}=90\cdot {0.5444444444444444}^6=90\cdot 0.026044823792293018=2.3440341413063717$$

$$a_8=a_1·r^{n-1}=90\cdot {0.5444444444444444}^{8-1}=90\cdot {0.5444444444444444}^7=90\cdot 0.01417995962024842=1.2761963658223576$$

$$a_9=a_1·r^{n-1}=90\cdot {0.5444444444444444}^{9-1}=90\cdot {0.5444444444444444}^8=90\cdot 0.007720200237690805=0.6948180213921725$$

$$a_{10}=a_1·r^{n-1}=90\cdot {0.5444444444444444}^{10-1}=90\cdot {0.5444444444444444}^9=90\cdot 0.004203220129409438=0.3782898116468494$$