Find the 30^th term of the sequence :

$\dfrac{1}{2}, 1, \dfrac{3}{2}, ………$

Since, $1 - \dfrac{1}{2} = \dfrac{1}{2}, \dfrac{3}{2} - 1 = \dfrac{1}{2}$.

Hence, the series is an A.P. with common difference = $\dfrac{1}{2}$.

We know that n^th term of an A.P. is given by,

⇒ a_n = a + (n - 1)d, where a is the first term.

So, 30^th term is,

$\Rightarrow a_{30} = \dfrac{1}{2} + (30 - 1) \times \dfrac{1}{2} \\[1em] = \dfrac{1}{2} + \dfrac{29}{2} \\[1em] = \dfrac{30}{2} \\[1em] = 15.$

Hence, 30^th term of the sequence = 15.