Introduction to Sequences Flashcards

All 5 cards in this deck

What is a term-to-term rule for a sequence?

A rule that gives each term from the previous term.
e.g. "first term 3, add 4 each time" gives $3, 7, 11, \dots$

What is a position-to-term rule ($n$th term rule)?

A rule that gives a term directly from its position number $n$.
e.g. $n$th term $=5n+2$, so the 3rd term is $5\times3+2=17$

What are the steps to generate the first three terms from an $n$th term rule?

e.g. $n$th term $=3n-1$

1. Substitute $n=1$: $3(1)-1=2$
2. Substitute $n=2$: $3(2)-1=5$
3. Substitute $n=3$: $3(3)-1=8$
   Sequence: $2, 5, 8$

In sequence notation, what does $u_{n+1}$ mean?

e.g. $u_{n+1}=2u_n+1$ with $u_1=3$

The term after $u_n$, i.e. the next term.
Here $u_2=2\times3+1=7$

True or false? A term-to-term rule on its own is enough to write out a sequence.

False. You also need the first term (or another given term) to start from.