పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=90$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=-0.9222222222222223$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=90$$

$$a_2=a_1·r^{n-1}=90\cdot -{0.9222222222222223}^{2-1}=90\cdot -{0.9222222222222223}^1=90\cdot -0.9222222222222223=-83$$

$$a_3=a_1·r^{n-1}=90\cdot -{0.9222222222222223}^{3-1}=90\cdot -{0.9222222222222223}^2=90\cdot 0.8504938271604939=76.54444444444445$$

$$a_4=a_1·r^{n-1}=90\cdot -{0.9222222222222223}^{4-1}=90\cdot -{0.9222222222222223}^3=90\cdot -0.7843443072702333=-70.590987654321$$

$$a_5=a_1·r^{n-1}=90\cdot -{0.9222222222222223}^{5-1}=90\cdot -{0.9222222222222223}^4=90\cdot 0.7233397500381041=65.10057750342938$$

$$a_6=a_1·r^{n-1}=90\cdot -{0.9222222222222223}^{6-1}=90\cdot -{0.9222222222222223}^5=90\cdot -0.6670799917018072=-60.03719925316265$$

$$a_7=a_1·r^{n-1}=90\cdot -{0.9222222222222223}^{7-1}=90\cdot -{0.9222222222222223}^6=90\cdot 0.6151959923472222=55.36763931125$$

$$a_8=a_1·r^{n-1}=90\cdot -{0.9222222222222223}^{8-1}=90\cdot -{0.9222222222222223}^7=90\cdot -0.5673474151646605=-51.06126736481944$$

$$a_9=a_1·r^{n-1}=90\cdot -{0.9222222222222223}^{9-1}=90\cdot -{0.9222222222222223}^8=90\cdot 0.5232203939851869=47.089835458666826$$

$$a_{10}=a_1·r^{n-1}=90\cdot -{0.9222222222222223}^{10-1}=90\cdot -{0.9222222222222223}^9=90\cdot -0.48252547445300575=-43.427292700770515$$