పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=90$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=1.4444444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=90$$

$$a_2=a_1·r^{n-1}=90\cdot {1.4444444444444444}^{2-1}=90\cdot {1.4444444444444444}^1=90\cdot 1.4444444444444444=130$$

$$a_3=a_1·r^{n-1}=90\cdot {1.4444444444444444}^{3-1}=90\cdot {1.4444444444444444}^2=90\cdot 2.0864197530864197=187.77777777777777$$

$$a_4=a_1·r^{n-1}=90\cdot {1.4444444444444444}^{4-1}=90\cdot {1.4444444444444444}^3=90\cdot 3.0137174211248285=271.2345679012346$$

$$a_5=a_1·r^{n-1}=90\cdot {1.4444444444444444}^{5-1}=90\cdot {1.4444444444444444}^4=90\cdot 4.353147386069196=391.78326474622764$$

$$a_6=a_1·r^{n-1}=90\cdot {1.4444444444444444}^{6-1}=90\cdot {1.4444444444444444}^5=90\cdot 6.287879557655506=565.9091601889955$$

$$a_7=a_1·r^{n-1}=90\cdot {1.4444444444444444}^{7-1}=90\cdot {1.4444444444444444}^6=90\cdot 9.082492694391286=817.4243424952158$$

$$a_8=a_1·r^{n-1}=90\cdot {1.4444444444444444}^{8-1}=90\cdot {1.4444444444444444}^7=90\cdot 13.119156114120747=1180.724050270867$$

$$a_9=a_1·r^{n-1}=90\cdot {1.4444444444444444}^{9-1}=90\cdot {1.4444444444444444}^8=90\cdot 18.949892164841078=1705.4902948356971$$

$$a_{10}=a_1·r^{n-1}=90\cdot {1.4444444444444444}^{10-1}=90\cdot {1.4444444444444444}^9=90\cdot 27.372066460326=2463.48598142934$$