Continuing Sequences Flashcards

All 5 cards in this deck

What are the steps to continue a sequence given a term-to-term rule?

e.g. $2, 5, 11, 23$ with rule "multiply the previous term by $2$ then add $1$"

1. Take the last term given: $23$.
2. Apply the rule to it: $23 \times 2 = 46$, $46 + 1 = 47$.
3. Write it as the next term: 5th term $= 47$.

How do you describe the rule for continuing an arithmetic sequence?

e.g. $5, 11, 17, 23$

State what is added (or subtracted) each time.
"Add $6$" — so the next term is $29$.

How do you continue a Fibonacci type sequence?

e.g. $3, 3, 6, 9, 15$

Add the two previous terms.
$9 + 15 = 24$ and $15 + 24 = 39$.

True or false? Every sequence has the same difference between one term and the next.

False. Only arithmetic sequences do; others may multiply, or have changing differences.

True or false? "It goes up by $1$ each time" is an acceptable rule for the sequence $1, 2, 4, 7, 11$.

False. The differences go up by $1$ each time ($+1, +2, +3, +4$), not the terms.