Flashcards: Sequences and Recurrence Relations — 11 cards

How can a sequence be defined explicitly?

By a formula like $u_n=\frac{n}{n+1}$.

Sequence notation label

Explicit or recursive definition

What is the first step to calculate terms of a recursive sequence?

Start from the given initial term(s).

Arithmetic sequence formula

$u_{n+1} = u_n + r$

What defines an arithmetic sequence?

Adding the same number called common difference to each term gives the next term.

Arithmetic sum formula

n(n+1)/2 for sum 1 to n

What is the explicit formula for an arithmetic sequence with first term $u_0$ and difference $r$?

$u_n = u_0 + rn$ for every natural number $n$.

Geometric sequence ratio

Same number q multiplies previous term

Arithmetic sequence explicit form

u_0 + r * n

Recurrence model

Connects current and previous terms

Sum of powers of q

Sum from i=0 to n of q^i