Question

use dots to represent
12 and 18 as rectangle
3,6,10 as triangle​

tell me answer fast please

Answer 1

Answer:

This is the Triangular Number Sequence:

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

It is simply the number of dots in each triangular pattern:

triangular numbers

By adding another row of dots and counting all the dots we can

find the next number of the sequence.

The first triangle has just one dot.

The second triangle has another row with 2 extra dots, making 1 + 2 = 3

The third triangle has another row with 3 extra dots, making 1 + 2 + 3 = 6

The fourth has 1 + 2 + 3 + 4 = 10

etc!

How may dots in the 60th triangle?

A Rule

We can make a "Rule" so we can calculate any triangular number.

First, rearrange the dots like this:

triangular numbers 1 to 5

Then double the number of dots, and form them into a rectangle:

triangular numbers when doubled become n by n+1 rectangles

Now it is easy to work out how many dots: just multiply n by n+1

Dots in rectangle = n(n+1)

But remember we doubled the number of dots, so

Dots in triangle = n(n+1)/2

We can use xn to mean "dots in triangle n", so we get the rule:

Rule: xn = n(n+1)/2

HOPE IT HELPS YOU

Answer 2

Answer:

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