समाधान - ज्यामितीय श्रृंखलाएं

श्रृंखला के आम रूप का पता लगाने के लिए, पहले पद: $$a=42$$ और सामान्य अनुपात: $$r=0.047619047619047616$$ को ज्यामितीय श्रृंखला के सूत्र में डालें:

$$a_1=42$$

$$a_2=a_1·r^{n-1}=42\cdot {0.047619047619047616}^{2-1}=42\cdot {0.047619047619047616}^1=42\cdot 0.047619047619047616=2$$

$$a_3=a_1·r^{n-1}=42\cdot {0.047619047619047616}^{3-1}=42\cdot {0.047619047619047616}^2=42\cdot 0.0022675736961451243=0.09523809523809522$$

$$a_4=a_1·r^{n-1}=42\cdot {0.047619047619047616}^{4-1}=42\cdot {0.047619047619047616}^3=42\cdot 0.00010797969981643449=0.004535147392290249$$

$$a_5=a_1·r^{n-1}=42\cdot {0.047619047619047616}^{5-1}=42\cdot {0.047619047619047616}^4=42\cdot 5.141890467449261E-06=0.00021595939963286898$$

$$a_6=a_1·r^{n-1}=42\cdot {0.047619047619047616}^{6-1}=42\cdot {0.047619047619047616}^5=42\cdot 2.448519270213934E-07=1.0283780934898523E-05$$

$$a_7=a_1·r^{n-1}=42\cdot {0.047619047619047616}^{7-1}=42\cdot {0.047619047619047616}^6=42\cdot 1.1659615572447303E-08=4.897038540427868E-07$$

$$a_8=a_1·r^{n-1}=42\cdot {0.047619047619047616}^{8-1}=42\cdot {0.047619047619047616}^7=42\cdot 5.552197891641572E-10=2.3319231144894604E-08$$

$$a_9=a_1·r^{n-1}=42\cdot {0.047619047619047616}^{9-1}=42\cdot {0.047619047619047616}^8=42\cdot 2.643903757924558E-11=1.1104395783283144E-09$$

$$a_{10}=a_1·r^{n-1}=42\cdot {0.047619047619047616}^{10-1}=42\cdot {0.047619047619047616}^9=42\cdot 1.2590017894878849E-12=5.287807515849116E-11$$