పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=144$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.4444444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=144$$

$$a_2=a_1·r^{n-1}=144\cdot {0.4444444444444444}^{2-1}=144\cdot {0.4444444444444444}^1=144\cdot 0.4444444444444444=64$$

$$a_3=a_1·r^{n-1}=144\cdot {0.4444444444444444}^{3-1}=144\cdot {0.4444444444444444}^2=144\cdot 0.19753086419753085=28.444444444444443$$

$$a_4=a_1·r^{n-1}=144\cdot {0.4444444444444444}^{4-1}=144\cdot {0.4444444444444444}^3=144\cdot 0.08779149519890259=12.641975308641973$$

$$a_5=a_1·r^{n-1}=144\cdot {0.4444444444444444}^{5-1}=144\cdot {0.4444444444444444}^4=144\cdot 0.039018442310623375=5.6186556927297655$$

$$a_6=a_1·r^{n-1}=144\cdot {0.4444444444444444}^{6-1}=144\cdot {0.4444444444444444}^5=144\cdot 0.01734152991583261=2.4971803078798955$$

$$a_7=a_1·r^{n-1}=144\cdot {0.4444444444444444}^{7-1}=144\cdot {0.4444444444444444}^6=144\cdot 0.007707346629258937=1.109857914613287$$

$$a_8=a_1·r^{n-1}=144\cdot {0.4444444444444444}^{8-1}=144\cdot {0.4444444444444444}^7=144\cdot 0.0034254873907817495=0.4932701842725719$$

$$a_9=a_1·r^{n-1}=144\cdot {0.4444444444444444}^{9-1}=144\cdot {0.4444444444444444}^8=144\cdot 0.001522438840347444=0.21923119301003194$$

$$a_{10}=a_1·r^{n-1}=144\cdot {0.4444444444444444}^{10-1}=144\cdot {0.4444444444444444}^9=144\cdot 0.000676639484598864=0.09743608578223642$$