A matches seller arranged his matchbox in a triangular pattern, he continues until there are 11 matchboxes in the bottom row of the triangle. How many matchboxes are in the complete pattern?
1+2+3+...+11 = 11*12/2 = 66
read up on "triangular numbers"
Can I please get the solution
12*11 =2S S=132\2 =66
The answer
To determine the number of matchboxes in the complete pattern, we need to find the sum of the matchboxes in each row of the triangular pattern.
We know that in a triangular pattern, each row has one more matchbox than the row above it. So, the number of matchboxes in each row follows a pattern: 1, 2, 3, 4, and so on.
To find the sum of matchboxes in all the rows, we need to add the number of matchboxes in each row.
The number of matchboxes in each row can be determined by finding the sum of numbers from 1 to 11, as the bottom row has 11 matchboxes.
To find the sum of numbers from 1 to 11, you can use the arithmetic sum formula: Sn = n/2 * (a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term.
Substituting the known values:
n = 11
a = 1
l = 11
Sn = 11/2 * (1 + 11) = 11/2 * 12 = 6 * 12 = 72
So, the sum of the matchboxes in all the rows is 72.
However, this sum represents the number of matchboxes in the complete triangular pattern, counting each matchbox only once. To find the total number of matchboxes including all repetitions in the triangular pattern, we need to square the number of matchboxes in the bottom row.
The number of matchboxes in the bottom row is 11, so the total number of matchboxes in the complete pattern is 11 * 11 = 121.
Therefore, there are 121 matchboxes in the complete triangular pattern.