Sofia and Zara are looking at the sequence $4, 8, 20, 56, 164, ...$

Sofia says: Term-to-term rule is 'Add $4$'.

Zara says: Term-to-term rule is 'Multiply by $2$'.

They are both incorrect. Explain why.

What must Sofia and Zara do to answer the question correctly?

In general, how many terms of a sequence must you know to be able to work out the term-to-term rule?

What are the term-to-term rules for the sequence $2, 6, ...$ and $3, 10, ...$?

Write down three possible term-to-term rules for the sequence and work out the next two terms for each rule.

$3, 7, ...$

Write down three possible term-to-term rules for the sequence and work out the next two terms for each rule.

$4, 8, ...$

Write down three possible term-to-term rules for the sequence and work out the next two terms for each rule.

$2, 9, ...$

Write down three possible term-to-term rules for the sequence and work out the next two terms for each rule.

$7, 17, ...$

The second term of a sequence is $13$. The term-to-term rule is: ‘Multiply by $2$ then subtract $3$’. What is the first term of the sequence?