Quick Answer: Can A Triangular Number Be A Square Number Explain?

Which of the following numbers is a square number as well as a triangular number?

The triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, 45, …

and so on, given by the formula n(n+1)/2.

Notice that the numbers 1 and 36 on this list are perfect squares as well as triangular..

Is 4851 a triangular number?

If you double a triangular number, you get a rectangular number. … 98 and 99 work, so 4851 is the 98th triangle number.

What does three numbers in a triangle mean?

Triangular numbers get their name from the shape made when a series of dots are used to create equilateral triangles. The first four “dot” triangles can be seen in the photo with the corresponding triangular numbers represented underneath. The numbers represent the addition of all the dots in the triangle.

What is the mean of first five triangular numbers?

This is the Triangular Number Sequence: 1, 3, 6, 10, 15, 21, 28, 36, 45, …

How do you know if a number is a triangular number?

A number is termed as triangular number if we can represent it in the form of triangular grid of points such that the points form an equilateral triangle and each row contains as many points as the row number, i.e., the first row has one point, second row has two points, third row has three points and so on.

What are the triangular numbers from 1 to 100?

The triangular numbers up to 100 are 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91 — so what’s next? Perfect Numbers These are the numbers which equal the sum of all of their smaller factors. They are few and far between — in fact, nobody knows how many there are. Only 47 perfect numbers are currently known.

What is the meaning of a square number?

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it can be written as 3 × 3. … Square numbers are non-negative.

What does a triangular number mean?

: a number (such as 3, 6, 10, 15) representable by that many dots arranged in rows that form a triangle and that equals n(n+1)2 for some positive integer value of n.

Why 1 is a triangular number?

Triangular numbers have that name because, if drawn as dots they can form a triangle. But 1 is just a single dot, so it can’t be a triangular number, can it???

Is 25 a triangular number?

A triangular number is a number that is the sum of all of the natural numbers up to a certain number. For example, 10 is a triangular number because 1 + 2 + 3 + 4 = 10. The first 25 triangular numbers are:0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300.

What is the first rectangular number?

The numbers that can be arranged to form a rectangle are called Rectangular Numbers (also known as Pronic numbers). The first few rectangular numbers are: 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462 . . . . . . Given a number n, find n-th rectangular number.

What is the 1000th triangular number?

Half of those dots were in the original triangle, so the 1000th triangular number is (1000 x 1001)/2 = 500500.