Quadratic Sequences Flashcards

All 5 cards in this deck

What is the general form of the $n$th term of a quadratic sequence?

$an^2+bn+c$, where $a\neq0$.

How do you get the coefficient of $n^2$ from the second difference of a quadratic sequence?

e.g. constant second difference $4$

Halve the second difference: $a=\tfrac{4}{2}=2$, so the $n$th term contains $2n^2$.

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

e.g. $3, 9, 17, 27$

1. Second difference is $2$, so halve it: the $n^2$ term is $n^2$
2. Subtract $1, 4, 9, 16$ from the terms: $2, 5, 8, 11$, which has $n$th term $3n-1$
3. $n$th term $=n^2+3n-1$

True or false? In a quadratic sequence the first differences are constant.

False. The second differences are constant; the first differences change by a fixed amount.

What are the steps to find unknown coefficients in an $n$th term rule from given terms?

e.g. $n$th term $=an^2+bn$, 2nd term $=-2$, 4th term $=12$

1. Substitute $n=2$: $4a+2b=-2$
2. Substitute $n=4$: $16a+4b=12$
3. Solve the two equations together: $a=2$, $b=-5$