nth Terms of Linear Sequences Flashcards

All 7 cards in this deck

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

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

1. Find the common difference: $6$, so start with $6n$.
2. Compare $6n$ ($6, 12, 18$) with the terms: each is $1$ less.
3. $n$th term $= 6n - 1$.

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

The common difference. It is negative if the sequence decreases.
e.g. $20, 17, 14$ has $n$th term $23 - 3n$.

How do you decide whether a given number is a term of a sequence?

e.g. is $85$ a term of the sequence with $n$th term $8n + 16$?

Set the $n$th term equal to the number and solve for $n$; it is a term only if $n$ is a positive whole number.
$8n + 16 = 85$ gives $n = 8.625$, so $85$ is not a term.

How do you find an expression in terms of $n$ for the number of tiles in pattern number $n$?

e.g. patterns needing $4, 8, 12, 16$ tiles

Treat the numbers of tiles as a linear sequence and find its $n$th term.
Difference $4$ and no adjustment needed, so $4n$.

True or false? Every term of the sequence with $n$th term $2n + 1$ is odd.

True. $2n$ is always even, and even $+\,1$ is odd.

How do you find the position of a given number in a sequence?

e.g. the $n$th term is $4n + 3$ — which term is $39$?

1. Put the $n$th term equal to the number: $4n + 3 = 39$
2. Solve for $n$: $n = 9$
3. $n$ is the position: $39$ is the 9th term.

In a linear sequence, how do you find the difference between the 5th term and the 7th term without working out both terms?

e.g. the $n$th term is $6n + 31$

Multiply the common difference by the gap in positions: $6 \times 2 = 12$.