పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=99$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=1.4444444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=99$$

$$a_2=a_1·r^{n-1}=99\cdot {1.4444444444444444}^{2-1}=99\cdot {1.4444444444444444}^1=99\cdot 1.4444444444444444=143$$

$$a_3=a_1·r^{n-1}=99\cdot {1.4444444444444444}^{3-1}=99\cdot {1.4444444444444444}^2=99\cdot 2.0864197530864197=206.55555555555554$$

$$a_4=a_1·r^{n-1}=99\cdot {1.4444444444444444}^{4-1}=99\cdot {1.4444444444444444}^3=99\cdot 3.0137174211248285=298.358024691358$$

$$a_5=a_1·r^{n-1}=99\cdot {1.4444444444444444}^{5-1}=99\cdot {1.4444444444444444}^4=99\cdot 4.353147386069196=430.96159122085044$$

$$a_6=a_1·r^{n-1}=99\cdot {1.4444444444444444}^{6-1}=99\cdot {1.4444444444444444}^5=99\cdot 6.287879557655506=622.5000762078951$$

$$a_7=a_1·r^{n-1}=99\cdot {1.4444444444444444}^{7-1}=99\cdot {1.4444444444444444}^6=99\cdot 9.082492694391286=899.1667767447373$$

$$a_8=a_1·r^{n-1}=99\cdot {1.4444444444444444}^{8-1}=99\cdot {1.4444444444444444}^7=99\cdot 13.119156114120747=1298.796455297954$$

$$a_9=a_1·r^{n-1}=99\cdot {1.4444444444444444}^{9-1}=99\cdot {1.4444444444444444}^8=99\cdot 18.949892164841078=1876.0393243192666$$

$$a_{10}=a_1·r^{n-1}=99\cdot {1.4444444444444444}^{10-1}=99\cdot {1.4444444444444444}^9=99\cdot 27.372066460326=2709.834579572274$$