Roshani reads 1/6 hours on the first day 1/4 hours on the second day and 1/3 hours on the third day.if the pattern continues,how long will she read on 5thh day?please fast tomorrow is my exam!

On the second day she reads 1/4 hours

On the third day she reads 1/3 hours

So the pattern will be as $\frac{1}{6},\frac{1}{4},\frac{1}{3},...$

S, the given pattern shows an arithmetic progression in which common difference is given by;

$d=\frac{1}{3}-\frac{1}{4}=\frac{1}{4}-\frac{1}{6}=\frac{1}{12}$

First term;

*a*= $\frac{1}{6}$ and for 5th day,

*n*= 5

So, nth term = ${t}_{n}=a+\left(n-1\right)d$

Then, 5th term = ${t}_{5}=\frac{1}{6}+\left(5-1\right)\times \frac{1}{12}=\frac{1}{6}+\frac{1}{3}=\frac{3}{6}=\frac{1}{2}$

Therefore, on 5th day Roshni reads $\frac{1}{2}$ hours.

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