పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=72$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=1.9444444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=72$$

$$a_2=a_1·r^{n-1}=72\cdot {1.9444444444444444}^{2-1}=72\cdot {1.9444444444444444}^1=72\cdot 1.9444444444444444=140$$

$$a_3=a_1·r^{n-1}=72\cdot {1.9444444444444444}^{3-1}=72\cdot {1.9444444444444444}^2=72\cdot 3.780864197530864=272.2222222222222$$

$$a_4=a_1·r^{n-1}=72\cdot {1.9444444444444444}^{4-1}=72\cdot {1.9444444444444444}^3=72\cdot 7.351680384087791=529.3209876543209$$

$$a_5=a_1·r^{n-1}=72\cdot {1.9444444444444444}^{5-1}=72\cdot {1.9444444444444444}^4=72\cdot 14.294934080170705=1029.235253772291$$

$$a_6=a_1·r^{n-1}=72\cdot {1.9444444444444444}^{6-1}=72\cdot {1.9444444444444444}^5=72\cdot 27.795705155887482=2001.2907712238987$$

$$a_7=a_1·r^{n-1}=72\cdot {1.9444444444444444}^{7-1}=72\cdot {1.9444444444444444}^6=72\cdot 54.047204469781214=3891.3987218242473$$

$$a_8=a_1·r^{n-1}=72\cdot {1.9444444444444444}^{8-1}=72\cdot {1.9444444444444444}^7=72\cdot 105.09178646901903=7566.60862576937$$

$$a_9=a_1·r^{n-1}=72\cdot {1.9444444444444444}^{9-1}=72\cdot {1.9444444444444444}^8=72\cdot 204.34514035642587=14712.850105662663$$

$$a_{10}=a_1·r^{n-1}=72\cdot {1.9444444444444444}^{10-1}=72\cdot {1.9444444444444444}^9=72\cdot 397.3377729152725=28608.319649899622$$