How many numbers lie between 10 and 300, whic | vedclass

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(C) The numbers between $10$ and $300$ that leave a remainder of $3$ when divided by $4$ form an Arithmetic Progression $(AP)$.The first number greate

Vedclass · Accepted Answer

$73$

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(C) The numbers between $10$ and $300$ that leave a remainder of $3$ when divided by $4$ form an Arithmetic Progression $(AP)$.The first number greater than $10$ that satisfies the condition is $11$ (since $11 = 4 	imes 2 + 3$).The last number less than $300$ that satisfies the condition is $299$ (since $299 = 4 	imes 74 + 3$).Thus,the sequence is $11, 15, 19, 23, \dots, 299$.In this $AP$,the first term $a = 11$,the common difference $d = 4$,and the last term $a_n = 299$.Using the formula for the $n^{th}$ term of an $AP$: $a_n = a + (n - 1)d$.Substituting the values: $299 = 11 + (n - 1)4$.$299 - 11 = (n - 1)4$.$288 = (n - 1)4$.$n - 1 = 288 / 4$.$n - 1 = 72$.$n = 73$.Therefore,there are $73$ such numbers.

How many numbers lie between $10$ and $300,$ which when divided by $4$ leave a remainder $3?$

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