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How many numbers lie between 10 and 300 which divided by 4 leave a remainder 3 |
| Answer» The numbers lying between 10 and 300, which when divided by 4 leave a remainder 3 are11, 15, 19............,299This is an A.P. with a = 11, d = 4 and l = 299Let the number of terms be n.then, an = 299{tex}\\Rightarrow{/tex}\xa0a + (n - 1)d = 299{tex}\\Rightarrow{/tex}\xa011 + (n - 1)4 = 299{tex}\\Rightarrow{/tex}\xa0(n - 1)4 = 288{tex}\\Rightarrow{/tex}\xa0n - 1 = 72{tex}\\Rightarrow{/tex}\xa0n = 73Thus, the required number of terms are 73. | |