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.
$11, 15, 19, 23, ...., 299.$
Here, first term $(a) = 11,$
Common differnce $(d) = 15 - 11 = 4$
$n^{th}$ term, $a_n = a + (n - 1)d =$ l[last term]
$\Rightarrow 299 = 11 + (n - 1)4$
$\Rightarrow 299 - 11 = (n - 1)4$
$\Rightarrow 4(n - 1) = 288$
$\Rightarrow (n - 1) = 72$
$n = 73.$
Last term before 300 is 299, which divided by 4 leave remainder 3.
$11, 15, 19, 23, ...., 299.$
Here, first term $(a) = 11,$
Common differnce $(d) = 15 - 11 = 4$
$n^{th}$ term, $a_n = a + (n - 1)d =$ l[last term]
$\Rightarrow 299 = 11 + (n - 1)4$
$\Rightarrow 299 - 11 = (n - 1)4$
$\Rightarrow 4(n - 1) = 288$
$\Rightarrow (n - 1) = 72$
$n = 73.$
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