if you 99 lines on a piece of paper so that no two lines are parallel to each other and mo three lines pass through the same point,how many times will they intersect?
n-1/2
To determine the number of intersections, we can use a formula based on combinatorics. Let's break it down step by step:
Step 1: Consider the first line. It will intersect with the other 98 remaining lines.
Step 2: Now, move on to the second line. It intersects with the 97 remaining lines, excluding the already counted intersection with the first line.
Step 3: Continuing in this manner, each subsequent line intersects with one less line from the remaining ones.
Step 4: Sum up the intersections for each line, starting from the first line.
Using the sum of arithmetic sequence formula, we can calculate the number of intersections:
Sum = (n/2) × (first term + last term)
Here, n represents the number of terms in the sequence, and the first and last terms are the number of intersections of the first and last lines, respectively.
Applying this formula, we get:
Sum = (99/2) × (1 + 97) = 49.5 × 98 = 4851
Therefore, the 99 lines will intersect 4851 times in total.