Question

Find the 37th term of the AP $6,7\frac{3}{4},9\frac{1}{2},11\frac{1}{4},...$

Answer 1

The given AP is $6,7\frac{3}{4},9\frac{1}{2},11\frac{1}{4},...$
First term, a = 6 and common difference, d $=7\frac{3}{4}-6\Rightarrow \frac{31}{4}-6\Rightarrow \frac{31-24}{4}=\frac{7}{4}$
$$\begin{gathered} \mathrm{Now},T_{37}=a+(37-1)d=a+36d \\ =6+36\times \frac{7}{4}=6+63=69 \\ \therefore {37}^{th}\mathrm{term}=69 \end{gathered}$$