Closed Sequences.

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Presentation transcript:

Closed Sequences

Sequences The values in the range are called the terms of the sequence. Domain: 1 2 3 4…....n Range: a1 a2 a3 a4….. an A sequence can be specified by an equation or rule.

Find the first 5 Terms of the Sequence an = 2n – 3 Find a1, a2, a3, a4, a5 a1 = -1 First Term a2 = 1 Second Term a3 = 3 Third Term a4 = 5 Fourth Term a5 = 7 Fifth Term

Find the first 5 Terms of the Sequence an = n3 – 20 Find a1, a2, a3, a4, a5 a1 = First Term a2 = Second Term a3 = Third Term a4 = Fourth Term a5 = Fifth Term -19 -12 7 44 105

Arithmetic Sequences will have a constant common difference.

Tell whether the sequence 2, 11, 20, 29, 38, … is arithmetic. Yes because each common difference is 9.

Tell whether the sequence 4, 8, 16, 22, 32, … is arithmetic. No because the difference is not constant.

Closed Sequences

Write the rule Example: 3, 5, 7, 9, ... an = 2n + 1

Write the rule Example: 65, 60, 55, 50, ... an = -5n + 70

Write the rule Example: 2, 6, 10, 14, … an = 4n – 2

What is the 50th term? Example: 1, 5, 9, 13, ... Substitute 50 in as an

What is the 18th term? Example: 100, 93, 86, 79... Substitute 18 in as an

To Write a Recursive Rule a1 = ___ an = an-1 d + -

Write the first 6 terms of the sequence Write the first 6 terms of the sequence. Then state the domain and range a1 = 3 an = -2an-1

Write a recursive rule for the following 38, 27, 16, 5, -4…

Write a recursive rule for the following 4, 8, 12, 16, 20…

RECURSIVE CLOSED an-1 n an = a1 +(n-1)d Need First Term an = an-1 (+-x÷) P a1 = ___ Plug in right side numbers n an = a1 +(n-1)d