పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=33$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.6060606060606061$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=33$$

$$a_2=a_1·r^{n-1}=33\cdot {0.6060606060606061}^{2-1}=33\cdot {0.6060606060606061}^1=33\cdot 0.6060606060606061=20$$

$$a_3=a_1·r^{n-1}=33\cdot {0.6060606060606061}^{3-1}=33\cdot {0.6060606060606061}^2=33\cdot 0.36730945821854916=12.121212121212123$$

$$a_4=a_1·r^{n-1}=33\cdot {0.6060606060606061}^{4-1}=33\cdot {0.6060606060606061}^3=33\cdot 0.22261179285972676=7.346189164370983$$

$$a_5=a_1·r^{n-1}=33\cdot {0.6060606060606061}^{5-1}=33\cdot {0.6060606060606061}^4=33\cdot 0.13491623809680411=4.452235857194536$$

$$a_6=a_1·r^{n-1}=33\cdot {0.6060606060606061}^{6-1}=33\cdot {0.6060606060606061}^5=33\cdot 0.08176741702836612=2.698324761936082$$

$$a_7=a_1·r^{n-1}=33\cdot {0.6060606060606061}^{7-1}=33\cdot {0.6060606060606061}^6=33\cdot 0.049556010320221895=1.6353483405673226$$

$$a_8=a_1·r^{n-1}=33\cdot {0.6060606060606061}^{8-1}=33\cdot {0.6060606060606061}^7=33\cdot 0.03003394564861933=0.991120206404438$$

$$a_9=a_1·r^{n-1}=33\cdot {0.6060606060606061}^{9-1}=33\cdot {0.6060606060606061}^8=33\cdot 0.018202391302193536=0.6006789129723867$$

$$a_{10}=a_1·r^{n-1}=33\cdot {0.6060606060606061}^{10-1}=33\cdot {0.6060606060606061}^9=33\cdot 0.011031752304359719=0.3640478260438707$$