Question

A sequence of numbers consists of natural numbers that are

not perfect squares. What is the 1000th member of this
sequence?

Answer 1

Given :

A sequence of numbers consists of natural numbers that are

not perfect squares.

To Find :

The 1000th member of this sequence .

Solution :

Now ,
`31^2=961` and
`32^2=1024` .

So , there are 31 numbers before 1000 which are perfect square .

Therefore , the
`999^(th)` is 1000+31 = 1031 .

Also , the first perfect square after 1000 is 32 .

So , we have to continue to 1031 + 1 = 1032 to compensate for the 32nd square.

Therefore , the 1000th member of this sequence is 1032 .

Hence , this is the required solution .