పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=405$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.4444444444444444$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=405$$

$$a_2=a_1·r^{n-1}=405\cdot {0.4444444444444444}^{2-1}=405\cdot {0.4444444444444444}^1=405\cdot 0.4444444444444444=180$$

$$a_3=a_1·r^{n-1}=405\cdot {0.4444444444444444}^{3-1}=405\cdot {0.4444444444444444}^2=405\cdot 0.19753086419753085=80$$

$$a_4=a_1·r^{n-1}=405\cdot {0.4444444444444444}^{4-1}=405\cdot {0.4444444444444444}^3=405\cdot 0.08779149519890259=35.55555555555555$$

$$a_5=a_1·r^{n-1}=405\cdot {0.4444444444444444}^{5-1}=405\cdot {0.4444444444444444}^4=405\cdot 0.039018442310623375=15.802469135802466$$

$$a_6=a_1·r^{n-1}=405\cdot {0.4444444444444444}^{6-1}=405\cdot {0.4444444444444444}^5=405\cdot 0.01734152991583261=7.023319615912206$$

$$a_7=a_1·r^{n-1}=405\cdot {0.4444444444444444}^{7-1}=405\cdot {0.4444444444444444}^6=405\cdot 0.007707346629258937=3.1214753848498695$$

$$a_8=a_1·r^{n-1}=405\cdot {0.4444444444444444}^{8-1}=405\cdot {0.4444444444444444}^7=405\cdot 0.0034254873907817495=1.3873223932666086$$

$$a_9=a_1·r^{n-1}=405\cdot {0.4444444444444444}^{9-1}=405\cdot {0.4444444444444444}^8=405\cdot 0.001522438840347444=0.6165877303407149$$

$$a_{10}=a_1·r^{n-1}=405\cdot {0.4444444444444444}^{10-1}=405\cdot {0.4444444444444444}^9=405\cdot 0.000676639484598864=0.27403899126253994$$