# Math

A triangular number is a number that can be represented by dots arranged in a triangular shape as shown below. The first four triangular numbers are 1,3,6,10. What is the 10th triangular number? the 20th? the 100th?
1st 2nd 3rd 4th
. . . .
. . . . . . . . . . . .
. . . .
Is there a simple formula for this?

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, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431

Search on Trianglular numbers on Google.

[k(k+1)]/2 is the general formula.
k=1 gives (1*2)/2=1
k=2 gives (2*3)/2=3
k=10 (10*11)/2 = something you can do.
k=20 (20*21)/2 = something you can do.
k=100 (100*101)/2 = something you can do.
Prove the formula by induction.

HELP MATH

1. 👍
2. 👎
3. 👁

## Similar Questions

1. ### Geometry

1.11 - Mr. Littles is building a triangular sandbox using three boards. He already has 2 boards that measure 9 feet and 12 feet. Select all of the values that could represent the length of the third board of his triangular

2. ### History

Which accurately describes the triangular trade? the triangular trade consisted of ships traveling from Spain to France, then to england, and back to Spain to trade goods such as weapons, maps, and works of arts the triangular

3. ### MATH

Which solid figure has 5 faces, 5 vertices, and 8 edges. Triangular pyramid Rectangular pyramid Pentagonal pyramid*** Triangular prism

4. ### problem in 3 dimensions

The Great Pyramid of Cheops at Giza in Egypt has a square base of side length 230 m. The angle of elevation of one triangular face is 52°. Determine the measure of the angle 𝜃 between the height and one of the edges where two

1. ### Math

Which of the following solid figures has the least number of vertices? (Triangular Pyramid) (Hexagonal pyramid) (cone) (triangular prism••)

2. ### History

Which accurately describes an aspect of the triangular trade during the 16th and 19th centuries? The triangular trade included European merchants, who purchased corn, tomatoes, cocoa, and tobacco from African tribal leaders in

3. ### geometry

If a triangular prism and a cylinder have the same height and the same volume, what must be true about their bases? The triangular prism has a larger base than the cylinder. Their bases have the same area. The cylinder has a

4. ### history

Which accurately describes the triangular trade? The triangular trade consisted of ships traveling from England to Africa, then to North America, and back to Western Europe to trade goods, spices, and slaves. The triangular trade

1. ### History

Which accurately describes the triangular trade? ANSWER: the triangular trade consisted of ships traveling from England to Africa, then to North America, and back to Western Europe to trade goods, spices, and slaves