Question:
Which term of the AP $\frac{5}{6}, 1,1 \frac{1}{6}, 1 \frac{1}{3}, \ldots .$ is 3 ?
Solution:
In the given $\mathrm{AP}$, first term $=\frac{5}{6}$ and common difference, $\mathrm{d}=\left(1-\frac{5}{6}=\frac{1}{6}\right)$.
Let its nth term be 3.
Now, $T_{n}=3$
$\Rightarrow a+(n-1) d=3$
$\Rightarrow \frac{5}{6}+(n-1) \times \frac{1}{6}=3$
$\Rightarrow \frac{2}{3}+\frac{n}{6}=3$
$\Rightarrow \frac{n}{6}=\frac{7}{3}$
$\Rightarrow n=14$
Hence, the 14th term of the given AP is 3.