# A.P series are given 3/4, 5/4, 7/4....... 99/4. Find the number of terms?

$\begin{array}{l}\text{Given series,}\\ 3/4,5/4,7/4.......99/4\\ \text{We know that, }l=a+\left(n-1\right)d\\ l=\frac{99}{4},\ a=\frac{3}{4},\ d=\left(\frac{5}{4}-\frac{3}{4}\right)=\frac{1}{2}\\ \frac{99}{4}=\frac{3}{4}+\left(n-1\right)\times\frac{1}{2}\\ \Rightarrow\frac{99}{4}-\frac{3}{4}=\left(n-1\right)\times\frac{1}{2}\\ \Rightarrow\frac{99-3}{4}\times2=n-1\\ \Rightarrow n=49\\ \text{There are 49 term in series.}\end{array}$

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