समाधान - ज्यामितीय श्रृंखलाएं

श्रृंखला के आम रूप का पता लगाने के लिए, पहले पद: $$a=42$$ और सामान्य अनुपात: $$r=0.07142857142857142$$ को ज्यामितीय श्रृंखला के सूत्र में डालें:

$$a_1=42$$

$$a_2=a_1·r^{n-1}=42\cdot {0.07142857142857142}^{2-1}=42\cdot {0.07142857142857142}^1=42\cdot 0.07142857142857142=3$$

$$a_3=a_1·r^{n-1}=42\cdot {0.07142857142857142}^{3-1}=42\cdot {0.07142857142857142}^2=42\cdot 0.00510204081632653=0.21428571428571427$$

$$a_4=a_1·r^{n-1}=42\cdot {0.07142857142857142}^{4-1}=42\cdot {0.07142857142857142}^3=42\cdot 0.0003644314868804664=0.01530612244897959$$

$$a_5=a_1·r^{n-1}=42\cdot {0.07142857142857142}^{5-1}=42\cdot {0.07142857142857142}^4=42\cdot 2.6030820491461885E-05=0.0010932944606413992$$

$$a_6=a_1·r^{n-1}=42\cdot {0.07142857142857142}^{6-1}=42\cdot {0.07142857142857142}^5=42\cdot 1.859344320818706E-06=7.809246147438565E-05$$

$$a_7=a_1·r^{n-1}=42\cdot {0.07142857142857142}^{7-1}=42\cdot {0.07142857142857142}^6=42\cdot 1.3281030862990755E-07=5.578032962456118E-06$$

$$a_8=a_1·r^{n-1}=42\cdot {0.07142857142857142}^{8-1}=42\cdot {0.07142857142857142}^7=42\cdot 9.486450616421968E-09=3.984309258897227E-07$$

$$a_9=a_1·r^{n-1}=42\cdot {0.07142857142857142}^{9-1}=42\cdot {0.07142857142857142}^8=42\cdot 6.77603615458712E-10=2.84593518492659E-08$$

$$a_{10}=a_1·r^{n-1}=42\cdot {0.07142857142857142}^{10-1}=42\cdot {0.07142857142857142}^9=42\cdot 4.840025824705085E-11=2.032810846376136E-09$$