పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=81$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=1.4444444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=81$$

$$a_2=a_1·r^{n-1}=81\cdot {1.4444444444444444}^{2-1}=81\cdot {1.4444444444444444}^1=81\cdot 1.4444444444444444=117$$

$$a_3=a_1·r^{n-1}=81\cdot {1.4444444444444444}^{3-1}=81\cdot {1.4444444444444444}^2=81\cdot 2.0864197530864197=169$$

$$a_4=a_1·r^{n-1}=81\cdot {1.4444444444444444}^{4-1}=81\cdot {1.4444444444444444}^3=81\cdot 3.0137174211248285=244.11111111111111$$

$$a_5=a_1·r^{n-1}=81\cdot {1.4444444444444444}^{5-1}=81\cdot {1.4444444444444444}^4=81\cdot 4.353147386069196=352.60493827160485$$

$$a_6=a_1·r^{n-1}=81\cdot {1.4444444444444444}^{6-1}=81\cdot {1.4444444444444444}^5=81\cdot 6.287879557655506=509.31824417009597$$

$$a_7=a_1·r^{n-1}=81\cdot {1.4444444444444444}^{7-1}=81\cdot {1.4444444444444444}^6=81\cdot 9.082492694391286=735.6819082456942$$

$$a_8=a_1·r^{n-1}=81\cdot {1.4444444444444444}^{8-1}=81\cdot {1.4444444444444444}^7=81\cdot 13.119156114120747=1062.6516452437804$$

$$a_9=a_1·r^{n-1}=81\cdot {1.4444444444444444}^{9-1}=81\cdot {1.4444444444444444}^8=81\cdot 18.949892164841078=1534.9412653521274$$

$$a_{10}=a_1·r^{n-1}=81\cdot {1.4444444444444444}^{10-1}=81\cdot {1.4444444444444444}^9=81\cdot 27.372066460326=2217.137383286406$$