Question

step 1 step 2 step 3 how many more line segments will be needed to be added to step 3 to create step 4 of the sequence? segments

Explanation:

Step1: Count line - segments in Step 3

Count the number of line - segments in Step 3. In Step 3, we can count the line - segments one by one. After counting, we find there are 13 line - segments.

Step2: Observe the pattern of growth

Notice that from Step 1 to Step 2, the number of new line - segments added is related to the number of end - points of the previous figure. Each end - point of the previous figure generates new line - segments. In Step 1, there are 2 end - points, and 4 new line - segments are added to get Step 2. In Step 2, there are 4 end - points, and 9 new line - segments are added to get Step 3.

Step3: Determine the number of end - points in Step 3

In Step 3, there are 8 end - points. Each of these 8 end - points will generate a new line - segment to form Step 4. So the number of new line - segments needed to go from Step 3 to Step 4 is 16.

Answer:

16