Question

Find the 30^th term of the sequence:

`1/2, 1, 3/2,.........`

Answer 1

The given sequence is `1/2, 1, 3/2,.........`

Now, 

`1- 1/2 = 1/2`

`3/2 - 1 = 1/2`, etc.

Hence, the given sequence is an A.P. with the first term a = `1/2 `

And common difference d = `1/2.`

The general term of an A.P. is given by

t_n = a + (n – 1)d

`=> t_30 = 1/2 + (30 - 1)(1/2)`

= `1/2 + 29 xx 1/2`

= `1/2 + 29/2`

= `30/2`

= 15 

So, the 30^th term is 15.