Answer:
The total number of ants in 15 lines is 240 ants.
The expression that allow us to calculate the total number of ants is [tex]T_a=n^2+n[/tex]
The expression that allow us to calculate the total number of ants at any row we choose is [tex]a=2n[/tex]
Step-by-step explanation:
We see that the total amount of ants is equal line number multiplied by the number of line increased by one. For example:
In two lines we have 2 ants in the first line and 4 in the second one, whose sum is equal 6. If we apply the logic of the above, we should multiply 2 (line number) by 3 (line number +1 ). We can check that 2×3=6.
To calculate the total amount of ants in all the lines, we can find out with the following expression:
[tex]T_a=n \times (n+1)[/tex]
or
[tex]T_a=n^2+n[/tex]
In 15 lines:
[tex]T_a=15^2+15=225+15=240[/tex]
In addition, the amount of ants in each line is double the previous one, so we can express the total number of ants in any row that we choose as:
a = 2n
