పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=90$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.2222222222222222$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=90$$

$$a_2=a_1·r^{n-1}=90\cdot {0.2222222222222222}^{2-1}=90\cdot {0.2222222222222222}^1=90\cdot 0.2222222222222222=20$$

$$a_3=a_1·r^{n-1}=90\cdot {0.2222222222222222}^{3-1}=90\cdot {0.2222222222222222}^2=90\cdot 0.04938271604938271=4.444444444444445$$

$$a_4=a_1·r^{n-1}=90\cdot {0.2222222222222222}^{4-1}=90\cdot {0.2222222222222222}^3=90\cdot 0.010973936899862823=0.987654320987654$$

$$a_5=a_1·r^{n-1}=90\cdot {0.2222222222222222}^{5-1}=90\cdot {0.2222222222222222}^4=90\cdot 0.002438652644413961=0.21947873799725648$$

$$a_6=a_1·r^{n-1}=90\cdot {0.2222222222222222}^{6-1}=90\cdot {0.2222222222222222}^5=90\cdot 0.000541922809869769=0.04877305288827921$$

$$a_7=a_1·r^{n-1}=90\cdot {0.2222222222222222}^{7-1}=90\cdot {0.2222222222222222}^6=90\cdot 0.00012042729108217089=0.01083845619739538$$

$$a_8=a_1·r^{n-1}=90\cdot {0.2222222222222222}^{8-1}=90\cdot {0.2222222222222222}^7=90\cdot 2.6761620240482418E-05=0.0024085458216434176$$

$$a_9=a_1·r^{n-1}=90\cdot {0.2222222222222222}^{9-1}=90\cdot {0.2222222222222222}^8=90\cdot 5.947026720107203E-06=0.0005352324048096483$$

$$a_{10}=a_1·r^{n-1}=90\cdot {0.2222222222222222}^{10-1}=90\cdot {0.2222222222222222}^9=90\cdot 1.3215614933571563E-06=0.00011894053440214406$$