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| 1. |
Find the sumof all multiples of 9 lying between 400 and 800 |
| Answer» The numbers divisible by 9 between 400 and 800 are:405, 414, 423,.................792Here a=414, d=9 and l=792Let the number of these terms be n, then{tex}\\mathrm{We}\\;\\mathrm{know}\\;\\mathrm{that}\\;{\\mathrm a}_{\\mathrm n}=\\mathrm a+(\\mathrm n-1)\\mathrm d{/tex}an=792Or, a + (n-1)d=792{tex}\\Rightarrow{/tex}\xa0405 + (n-1){tex}\\times{/tex}9=792{tex}\\Rightarrow{/tex}\xa09(n - 1) = 387{tex}\\Rightarrow{/tex}\xa0(n - 1) = 43{tex}\\Rightarrow{/tex}\xa0n = 44So, S44\xa0=\xa0{tex}\\frac{n}{2}{/tex}(a+l)\xa0=\xa0{tex}\\frac{{44}}{2}{/tex}(405\xa0+ 792)\xa0= 22\xa0{tex}\\times{/tex}\xa01197 = 26334Hence, Sn=26334 | |