6. Consider the sequence of shapes shown below. Step 1 Step 2 Step 3 Step 4...

 

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6. Consider the sequence of shapes shown below. Step 1 Step 2 Step 3 Step 4 The sequence starts with one triangle. Then at each step, triangles are attached to the outside of the preceding figure, one triangle per exposed edge. (a) Draw the next two figures in the sequence. (b) Make a table listing the number of triangles in each of the first 6 figures. Look for a pattern in the number of triangles. (Hint: Consider the number of triangles added at each step.) (c) Based on the pattern you observed, predict the number of triangles in the figure at step 7. (Draw the figure if you need to, to check your answer.) (d) How many triangles would there be in the 10th figure? (e) [Bonus] How many in the 20th figure? How many in the nth figure? [Hint: Try to find a pattern to describe 27(n).] 6. Consider the sequence of shapes shown below. Step 1 Step 2 Step 3 Step 4 The sequence starts with one triangle. Then at each step, triangles are attached to the outside of the preceding figure, one triangle per exposed edge. (a) Draw the next two figures in the sequence. (b) Make a table listing the number of triangles in each of the first 6 figures. Look for a pattern in the number of triangles. (Hint: Consider the number of triangles added at each step.) (c) Based on the pattern you observed, predict the number of triangles in the figure at step 7. (Draw the figure if you need to, to check your answer.) (d) How many triangles would there be in the 10th figure? (e) [Bonus] How many in the 20th figure? How many in the nth figure? [Hint: Try to find a pattern to describe 27(n).]