Question
How many numbers lie between $10$ and $300$, which when divided by $4$ leave a remainder $3$?
✓
Answer
Here, the first number is 11 , which divided by 4 leave remainder 3 between 10 and 300. Last term before 300 is 299 , which divided by 4 leave remainder 3 .
$\therefore 11,15,19,23 \ldots . . . . . .299$
Here, first term $(a)=11$, common difference $d=15-11=-4$
$\because n ^{\text {th }}$ term, $a_n=a+(n-1) d=1[$ last term]
$\Rightarrow 299 = 11 + (n - 1)4$
$\Rightarrow 299 - 11 = (n - 1)4$
$\Rightarrow 4(n - 1) = 288$
$\Rightarrow (n - 1) = 72$
$\therefore$ $n = 73$
$\therefore 11,15,19,23 \ldots . . . . . .299$
Here, first term $(a)=11$, common difference $d=15-11=-4$
$\because n ^{\text {th }}$ term, $a_n=a+(n-1) d=1[$ last term]
$\Rightarrow 299 = 11 + (n - 1)4$
$\Rightarrow 299 - 11 = (n - 1)4$
$\Rightarrow 4(n - 1) = 288$
$\Rightarrow (n - 1) = 72$
$\therefore$ $n = 73$
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