36 is a square number. Is it also a triangular number? If yes, which term of the sequence of triangular numbers is it?

36 is a square number. Is it also a triangular number? If yes, which term of the sequence of triangular numbers is it?

Question 1.

36 is a square number. Is it also a triangular number? If yes, which term of the sequence of triangular numbers is it?

Solution:

Yes, 36 is also a triangular number.

We have the following sequence of triangular numbers:

1, 3, 6, 10, 15, 21, 28, 36

Thus, it is the 8th term of the sequence of triangular numbers.

Question 2.

37 is an odd number. Is it also a hexagonal number? If yes, which term of the sequence of hexagonal numbers is it?

Solution:

Yes, 37 is also a hexagonal number.

We have the following sequence of hexagonal numbers:

1, 7, 19, 37, ...

So, 37 is the 4th term of the sequence of hexagonal numbers.

Question 3.

37 is an odd number. Is it also a triangular number? If yes, which term of the sequence of triangular numbers is it? If no, then which of the triangular numbers is nearest to 37?

Solution:

No, 37 is not a triangular number.

We have the following sequence of triangular numbers:

1, 3, 6, 10, 15, 21, 28, 36, 45, ...

Thus, the triangular number nearest to 37 is 36.