nth Terms of Linear Sequences Flashcards

All 7 cards in this deck

What is an arithmetic (linear) sequence?

A sequence where the same number, the common difference, is added each time.
e.g. $7, 13, 19, 25$ has common difference $6$

What are the steps to find the $n$th term of a linear sequence?

e.g. $1, 5, 9, 13$

1. Find the common difference: $4$, so start with $4n$
2. Compare $4n$ ($4, 8, 12$) with the terms: each is $3$ less
3. $n$th term $=4n-3$

In the $n$th term of a linear sequence, what does the number in front of $n$ tell you?

The common difference of the sequence.
e.g. $6n+1$ has common difference $6$

How do you use an $n$th term rule to find a later term?

e.g. the 100th term of $3n-2$

Substitute the position number for $n$.
$3\times100-2=298$

What are the steps to decide whether a number is a term of a sequence?

e.g. is $-58$ a term of the sequence with $n$th term $8-6n$?

1. Set the $n$th term equal to the number: $8-6n=-58$
2. Solve for $n$: $n=11$
3. $n$ is a positive integer, so yes, $-58$ is the 11th term

True or false? If solving "$n$th term $=k$" gives $n=4.5$, then $k$ is a term of the sequence.

False. $n$ must be a positive whole number, so $k$ is not a term.

True or false? A linear sequence with $n$th term $8-6n$ has terms that get smaller as $n$ increases.

True. The coefficient of $n$ is negative ($-6$), so each term is $6$ less than the one before.