పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=144$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=1.3194444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=144$$

$$a_2=a_1·r^{n-1}=144\cdot {1.3194444444444444}^{2-1}=144\cdot {1.3194444444444444}^1=144\cdot 1.3194444444444444=190$$

$$a_3=a_1·r^{n-1}=144\cdot {1.3194444444444444}^{3-1}=144\cdot {1.3194444444444444}^2=144\cdot 1.7409336419753085=250.69444444444443$$

$$a_4=a_1·r^{n-1}=144\cdot {1.3194444444444444}^{4-1}=144\cdot {1.3194444444444444}^3=144\cdot 2.297065222050754=330.7773919753086$$

$$a_5=a_1·r^{n-1}=144\cdot {1.3194444444444444}^{5-1}=144\cdot {1.3194444444444444}^4=144\cdot 3.0308499457614118=436.4423921896433$$

$$a_6=a_1·r^{n-1}=144\cdot {1.3194444444444444}^{6-1}=144\cdot {1.3194444444444444}^5=144\cdot 3.9990381228796408=575.8614896946683$$

$$a_7=a_1·r^{n-1}=144\cdot {1.3194444444444444}^{7-1}=144\cdot {1.3194444444444444}^6=144\cdot 5.276508634355081=759.8172433471317$$

$$a_8=a_1·r^{n-1}=144\cdot {1.3194444444444444}^{8-1}=144\cdot {1.3194444444444444}^7=144\cdot 6.9620600036629545=1002.5366405274655$$

$$a_9=a_1·r^{n-1}=144\cdot {1.3194444444444444}^{9-1}=144\cdot {1.3194444444444444}^8=144\cdot 9.186051393721954=1322.7914006959613$$

$$a_{10}=a_1·r^{n-1}=144\cdot {1.3194444444444444}^{10-1}=144\cdot {1.3194444444444444}^9=144\cdot 12.120484477827578=1745.3497648071711$$