Question

Which term of the A.P. `1, 1 1/6, 1 1/3`, ......, is 3?

Answer 1

The terms are $$1, \frac{7}{6}, \frac{4}{3}$$. 

Here $$a = 1$$ and $$d = \frac{7}{6} - 1 = \frac{1}{6}$$. 

Let the term be nth.

$$1 + (n - 1) \times \frac{1}{6} = 3$$

So $$\frac{n + 5}{6} = 3$$, giving $$n = 13$$. 

Hence 3 is the 13th term.