The nth term of a number sequence is n2-3 (a) Find the 4th term of this sequence.
b) Show that 40 is not a number in this sequence.

Here's the solution,

nth term = n² - 3

So, 4th term :

=》(4)² - 3

=》16 - 3

=》13

4th term of the sequence is 13

now, let's assume that 40 is a number in the sequence, then

=》40 = n² - 3

=》40 + 3 = n²

but, the term of the sequence should be a natural number, so our assumption was wrong, hence 40, can't be a number of this sequence.

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are