For the following exercises, write the first eight terms of the sequence. a1=2, a2=10, an=(2(an-

For the following exercises, write the first eight terms of...

Key Concepts

Sequence

A sequence is an ordered list of elements that follow a specific rule or pattern. In problems involving sequences, identifying and applying the rule enables the generation of successive terms.

Recurrence Relation

A recurrence relation is an equation that defines each term of a sequence in terms of one or more of its preceding terms. It provides a systematic way to compute subsequent terms from initial known values.

Initial Conditions

Initial conditions are the starting values provided for a sequence. They are essential to uniquely determine the sequence when using a recurrence relation as they serve as the base cases for the recursive computation.

Recursive Computation

Recursive computation refers to the method of calculating terms in a sequence by repeatedly applying a recurrence relation. It involves using previously computed terms to derive the next term, allowing the entire sequence to be built step by step.

Transcript

00:01 Alright, in this exercise, you are supposed to write the first eight terms of the sequence, and the first two are given to you.

00:06 Because notice in the recursive formula, you need the previous term, which would be this one, and the previous term, which would be this one.

00:16 So when i'm trying to find the third term, i plug in three here.

00:20 Three minus one is two, so this is a sub two.

00:23 A sub two is ten, and then three minus two would be one, a sub one is two.

00:31 So now i will plug in these numbers.

00:38 So for a sub three, i'm going to have two times 10 plus two divided by, and when i do the math, i get two times 12 divided by 2, which is 12.

01:00 A sub 4 is next okay and so i'll start making my list up here so a sub 1 was 2 a sub 2 was 10 and then i just got 12 and so now i will find the next term so a sub 4 will still be 2 but this time instead of 10 i'm going to put 12 there because that's my previous term plus 2 and then instead of 2 on the bottom i'm going to put 10 there because that's my previous previous term.

01:35 So then i get two times 14 divided by 10, which if i reduce that first, i get 14 -fiths.

01:55 And that's my next term.

02:00 All right, so now my fifth term will be two times the previous, which is 14 -fifths plus two divided by previous previous which is 12.

02:19 So now i do 14 fifth plus two times 12 divided by 12.

02:26 And i just was using my calculator.

02:28 I think it's pretty easy just to plug it all in...

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