పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=54$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=1.6481481481481481$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=54$$

$$a_2=a_1·r^{n-1}=54\cdot {1.6481481481481481}^{2-1}=54\cdot {1.6481481481481481}^1=54\cdot 1.6481481481481481=89$$

$$a_3=a_1·r^{n-1}=54\cdot {1.6481481481481481}^{3-1}=54\cdot {1.6481481481481481}^2=54\cdot 2.71639231824417=146.6851851851852$$

$$a_4=a_1·r^{n-1}=54\cdot {1.6481481481481481}^{4-1}=54\cdot {1.6481481481481481}^3=54\cdot 4.477016968957984=241.75891632373114$$

$$a_5=a_1·r^{n-1}=54\cdot {1.6481481481481481}^{5-1}=54\cdot {1.6481481481481481}^4=54\cdot 7.378787226615937=398.4545102372606$$

$$a_6=a_1·r^{n-1}=54\cdot {1.6481481481481481}^{6-1}=54\cdot {1.6481481481481481}^5=54\cdot 12.161334503126266=656.7120631688184$$

$$a_7=a_1·r^{n-1}=54\cdot {1.6481481481481481}^{7-1}=54\cdot {1.6481481481481481}^6=54\cdot 20.043680940337733=1082.3587707782376$$

$$a_8=a_1·r^{n-1}=54\cdot {1.6481481481481481}^{8-1}=54\cdot {1.6481481481481481}^7=54\cdot 33.03495562388997=1783.8876036900583$$

$$a_9=a_1·r^{n-1}=54\cdot {1.6481481481481481}^{9-1}=54\cdot {1.6481481481481481}^8=54\cdot 54.44650093567051=2940.1110505262072$$

$$a_{10}=a_1·r^{n-1}=54\cdot {1.6481481481481481}^{10-1}=54\cdot {1.6481481481481481}^9=54\cdot 89.73589969027175=4845.738583274675$$