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| 1. |
Find the sum of all natural numbers lying between 100 and 1000, which are multiple of 5 |
| Answer» According to question, series is 105, 110, 115, 120, ………, 995Here a = 105, d = 110 - 105 = 5\xa0and an = 995{tex}\\therefore{/tex} an = a + (n - 1)d{tex}\\Rightarrow 995 = 105 + ( n - 1 ) \\times 5{/tex}{tex}\\Rightarrow 995 - 105 = ( n - 1 ) \\times 5{/tex}{tex}\\Rightarrow \\frac { 890 } { 5 } = ( n - 1 ){/tex}{tex}\\Rightarrow{/tex}\xa0n = 178 + 1 = 179Now,\xa0{tex}\\mathrm { S } _ { n } = \\frac { n } { 2 } ( a + l ){/tex}{tex}\\Rightarrow S _ { 199 } = \\frac { 179 } { 2 } ( 105 + 995 ){/tex}{tex}\\Rightarrow S _ { 179 } = \\frac { 179 } { 2 } \\times 1100=98450{/tex} | |