పరిష్కారం - జ్యామితీ నిర్ణయాలు

శ్రేణికి సామాన్య రూపాన్ని కనుగొనడానికి, మొదటి పదాన్ని: $$a=72$$ మరియు పునరావృత్తి అనుపాతాన్ని: $$r=0.1388888888888889$$ జామితీయ శ్రేణుల సూత్రానికి ప్లగ్ చేయండి:

$$a_1=72$$

$$a_2=a_1·r^{n-1}=72\cdot {0.1388888888888889}^{2-1}=72\cdot {0.1388888888888889}^1=72\cdot 0.1388888888888889=10$$

$$a_3=a_1·r^{n-1}=72\cdot {0.1388888888888889}^{3-1}=72\cdot {0.1388888888888889}^2=72\cdot 0.019290123456790126=1.388888888888889$$

$$a_4=a_1·r^{n-1}=72\cdot {0.1388888888888889}^{4-1}=72\cdot {0.1388888888888889}^3=72\cdot 0.0026791838134430732=0.19290123456790126$$

$$a_5=a_1·r^{n-1}=72\cdot {0.1388888888888889}^{5-1}=72\cdot {0.1388888888888889}^4=72\cdot 0.0003721088629782046=0.02679183813443073$$

$$a_6=a_1·r^{n-1}=72\cdot {0.1388888888888889}^{6-1}=72\cdot {0.1388888888888889}^5=72\cdot 5.1681786524750645E-05=0.0037210886297820464$$

$$a_7=a_1·r^{n-1}=72\cdot {0.1388888888888889}^{7-1}=72\cdot {0.1388888888888889}^6=72\cdot 7.178025906215367E-06=0.0005168178652475064$$

$$a_8=a_1·r^{n-1}=72\cdot {0.1388888888888889}^{8-1}=72\cdot {0.1388888888888889}^7=72\cdot 9.969480425299122E-07=7.178025906215368E-05$$

$$a_9=a_1·r^{n-1}=72\cdot {0.1388888888888889}^{9-1}=72\cdot {0.1388888888888889}^8=72\cdot 1.3846500590693224E-07=9.96948042529912E-06$$

$$a_{10}=a_1·r^{n-1}=72\cdot {0.1388888888888889}^{10-1}=72\cdot {0.1388888888888889}^9=72\cdot 1.923125082040726E-08=1.3846500590693227E-06$$