Question
How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?
✓
Answer
Number between 10 and 300 , which when divided by 4 leave a remainder 3 will be 11, 15, 19, 23,..299
$
\begin{aligned}
& \text { Here, } a=11, d=15-11=4, I=299 \\
& \therefore T_n=1=a+(n-1) d \\
& 299=11+(n-1) \times 4 \\
& \Rightarrow 299-11=(n-1) 4 \\
& 4(n-1)=288 \\
& \Rightarrow n-1=\frac{288}{4}=72 \\
& \therefore n=72+1 \\
& =73 .
\end{aligned}
$
$
\begin{aligned}
& \text { Here, } a=11, d=15-11=4, I=299 \\
& \therefore T_n=1=a+(n-1) d \\
& 299=11+(n-1) \times 4 \\
& \Rightarrow 299-11=(n-1) 4 \\
& 4(n-1)=288 \\
& \Rightarrow n-1=\frac{288}{4}=72 \\
& \therefore n=72+1 \\
& =73 .
\end{aligned}
$
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