Will the number $78$ be in this sequence? Explain why or why not.

Write down a rule to find the next term of the sequence if you know the one before it.

Draw the next two shapes in the pattern and explain the pattern in words.

Determine what the ${20}^{\mathrm{th}}$ term in the sequence would be, without drawing it. How do you know?

Will the number $46$ be in this sequence? Explain why or why not.

Write down a rule to find the next term of the sequence if you know the one before it.

Draw the next two shapes in the sequence below and explain the pattern in words.

Will the number $100$ be in this sequence? Explain why or why not.

On squared paper, draw a pattern for the first five terms in the sequence that begins $2, 6, 10, ...$