Final Review on Sequences

These flashcards cover concepts from the final review on sequences, focusing on identifying sequences, writing recursive and explicit rules, and calculating series.

What type of sequence is 5, 12, 19, 26, 33,… and what is its recursive equation?

It is an arithmetic sequence with the recursive equation: a(n) = a(n-1) + 7.

What type of sequence is 1, 2, 4, 8, 16,… and what is its explicit equation?

It is a geometric sequence with the explicit equation: a(n) = 2^(n).

What are the first six terms of the function f(n) = f(n-1) with f(0) = 40?

The first six terms are 40, 40, 40, 40, 40, 40.

What is the recursive rule for the sequence defined by an = -10 + 4n?

The recursive rule is: a(n) = a(n-1) + 4.

What is the explicit rule for the sequence where a₁ = 20 and an = an-1 + 3?

The explicit rule is: a(n) = 20 + 3(n-1).

What is the explicit rule for the sequence with a₁ = -10 and an = 2an-1?

The explicit rule is: a(n) = -10 * (2^(n-1)).

Given a₂ = 12 and a₄ = 3, how do you write the geometric explicit sequence?

The explicit sequence is: a(n) = 12 * (0.5)^(n-2).

What is the rule for the nth term of the sequence given a₃ = 4 and r = 2?

The nth term rule is: a(n) = 4 * (2^(n-3)).

How do you find the sum of Σ 5?

The sum Σ 5 is determined by adding 5 for each term in the series, which depends on the upper limit of the summation.