పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=27$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=1.8148148148148149$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=27$$

$$a_2=a_1·r^{n-1}=27\cdot {1.8148148148148149}^{2-1}=27\cdot {1.8148148148148149}^1=27\cdot 1.8148148148148149=49$$

$$a_3=a_1·r^{n-1}=27\cdot {1.8148148148148149}^{3-1}=27\cdot {1.8148148148148149}^2=27\cdot 3.2935528120713307=88.92592592592592$$

$$a_4=a_1·r^{n-1}=27\cdot {1.8148148148148149}^{4-1}=27\cdot {1.8148148148148149}^3=27\cdot 5.977188436722045=161.38408779149523$$

$$a_5=a_1·r^{n-1}=27\cdot {1.8148148148148149}^{5-1}=27\cdot {1.8148148148148149}^4=27\cdot 10.84749012590297=292.8822333993802$$

$$a_6=a_1·r^{n-1}=27\cdot {1.8148148148148149}^{6-1}=27\cdot {1.8148148148148149}^5=27\cdot 19.686185784046135=531.5270161692456$$

$$a_7=a_1·r^{n-1}=27\cdot {1.8148148148148149}^{7-1}=27\cdot {1.8148148148148149}^6=27\cdot 35.726781608083726=964.6231034182606$$

$$a_8=a_1·r^{n-1}=27\cdot {1.8148148148148149}^{8-1}=27\cdot {1.8148148148148149}^7=27\cdot 64.8374925480038=1750.6122987961026$$

$$a_9=a_1·r^{n-1}=27\cdot {1.8148148148148149}^{9-1}=27\cdot {1.8148148148148149}^8=27\cdot 117.66804203156245=3177.037134852186$$

$$a_{10}=a_1·r^{n-1}=27\cdot {1.8148148148148149}^{10-1}=27\cdot {1.8148148148148149}^9=27\cdot 213.54570590913187=5765.73405954656$$