Using nth Terms of Sequences Flashcards

All 6 cards in this deck

In an nth term rule, what does $n$ stand for and what values can it take?

The position of the term; $n$ is a positive integer $1, 2, 3, \ldots$
e.g. 10th term of $5n - 2$ is $5 \times 10 - 2 = 48$

What are the steps to find the value of the first negative term of a sequence?
e.g. nth term $318 - 9n$

1. Set up the inequality: $318 - 9n < 0$
2. Solve for $n$ and round up to the next integer: $n > 35.3\ldots$, so $n = 36$
3. Substitute that $n$: $318 - 9 \times 36 = -6$

What are the steps to find the limiting value of a sequence as $n \to \infty$?
e.g. nth term $\dfrac{3n + 4}{n}$

1. Split the fraction: $3 + \dfrac{4}{n}$
2. Any term $\dfrac{k}{n} \to 0$ as $n \to \infty$
3. State what is left: limiting value $= 3$

What are the steps to decide whether a given number is a term of a sequence?
e.g. is 100 a term of the sequence with nth term $4n + 2$?

1. Set the nth term equal to the number: $4n + 2 = 100$
2. Solve for $n$: $n = 24.5$
3. It is a term only if $n$ is a positive integer: $24.5$ is not, so 100 is not a term.

True or false? To subtract the sequence with nth term $8n + 6$ from the one with nth term $42 - 3n$, you can write $42 - 3n - 8n + 6$.

False. The whole nth term must be bracketed: $42 - 3n - (8n + 6) = 36 - 11n$.

What are the steps to find the term number where two sequences have equal terms?

e.g. sequences with nth terms $3n + 2$ and $5n - 6$

1. Set the two nth terms equal: $3n + 2 = 5n - 6$
2. Solve for $n$: $2n = 8$, so $n = 4$