# maths

Using the following formula for a triangular number, verify that 1225 and 41 616 are triangular numbers. [Hint verify that there is an n for each number that satisfies the equation]

e.g., t5 = 15 =(5+1)/2
tn = n(n+1)/2

so, should I plug in 1225 and 41,616 and work the equation out? Somehow, I'm just reall confused by this problem. Could someone please be so kind as to help me?

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. no, find n for each. I will do one.

41,616= n(n+1)/2
83,232= n^2+n

put it in binomial form, and solve

n^2+n-83232=0

n= (-1+-sqrt 332929)/2= -1/2 +-288.5
n= 288, or n=-289

Now put them in the formula and verify. Normally, we restrict n to positive values, but your problem did not.

Now do the other number.

1. 👍
2. 👎
3. ℹ️
4. 🚩
👤
bobpursley
2. oh, okay! I'll try it out; thanks so much!

1. 👍
2. 👎
3. ℹ️
4. 🚩
3. sorry, but I don't get where you're getting "n= (-1+-sqrt 332929)/2= -1/2 +-288.5" could you please explain?

1. 👍
2. 👎
3. ℹ️
4. 🚩
4. 1) I made an error in the next to last line.
n=0,180,360....the 1 was a typo.

Now, how did I get n. It came from the binomial equation for the quadratic form

if

ax^2+bx + c=0, then

x= (-b+-sqrt(b^2-4ac))/2a

1. 👍
2. 👎
3. ℹ️
4. 🚩
👤
bobpursley
5. oh... okay, thanks for the correction and the explanation

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

which three-dimensional figure has all triangular faces? A. triangular prism B. triangular pyramid***i pick B.*** C. rectangular pyramid D. cone

2. ### MATH

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

3. ### 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

4. ### Math

What is the formula for finding the base of a triangular prism?

1. ### Algebra

what solid has 2 bases that are triangles and 3 lateral surfaces that are rectangles a- triangular pyramid b- rectangular prism c- triangular prism d- rectangular pyramid my answer is C

2. ### 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

3. ### Mathematics

The dimensions of a triangular prism are shown below each congruent base is a right triangle which measurement is closest to the total surface area of the triangular prism in square inches?

4. ### math

which three-dimensional figure has all triangular faces? A. triangular prism B. triangular pyramid***i pick B.*** C. rectangular pyramid D. cone

1. ### Math

Identify the solid formed by the given net. The middle and a triangle on each edge of the middle triangle. A. Triangular prism B. Triangular pyramid C. Cone D. Triangle Is the answer B? Thank you

2. ### Math

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

3. ### Math

A triangular number is a number that can be represented by dots arranged in a triangular shape. The first four triangular numbers are 1, 3, 6, 10. What is the 10 triangular number? The 20th? The 100th?

4. ### math

please can u tell me the term to term rule to this question 0,1,3,6,10,15,21 {nth} thank u Those are the triangular numbers, except your sequence started with 0 and we usually start with 1. 0= 1*(1-1)/2 term 1 1= 2*(2-1)/2 term 2