DQ Thurs 330 Arithmetic Sequence An arithmetic sequence

Arithmetic Sequence An arithmetic sequence is defined as a sequence in which there is

Is the given sequence arithmetic? If so, identify the common difference. 1. 2. 3.

Arithmetic Sequence Formula The 1 st number in the sequence. The common difference. an

Example 1: an = a 1 + (n – 1) • d Given the

Example 3: an = a 1 + (n – 1) • d Given the

Example 4: an = a 1 + (n – 1) • d Given the

Example 5: an = a 1 + (n – 1) • d Suppose you

Geometric Sequences An geometric sequence is defined as a sequence in which there is

Is the given sequence geometric? If so, identify the common ratio. 1. 2. 3.

Geometric Sequence Formula 1 st The number in the sequence. The same as the

Example 1: an = a 1 • r (n-1) Given the sequence 4, 28,

Example 2: an = a 1 • r (n-1) Given the sequence -2, 6,

Example 3: an = a 1 • r (n-1) Given the sequence 100, 83,

Example 5: an = a 1 • r (n-1) Suppose you want a reduced

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DQ – Thurs 3/30

Arithmetic Sequence An arithmetic sequence is defined as a sequence in which there is a common difference between consecutive terms. Comm on Differe nce = 5

Is the given sequence arithmetic? If so, identify the common difference. 1. 2. 3. 4. 2, 4, 8, 16, … 4, 6, 12, 18, 24, … 2, 5, 7, 12, … 48, 45, 42, 39, …

Arithmetic Sequence Formula The 1 st number in the sequence. The common difference. an = a 1 + (n – 1) • d The “nth” number in the sequence. Ex. a 5 is the 5 th number in the sequence. The same as the n in an. If you’re looking for the 5 th number in the sequence, n = 5.

Example 1: an = a 1 + (n – 1) • d Given the sequence -4, 5, 14, 23, 32, 41, 50, …, find the 14 th term.

Example 3: an = a 1 + (n – 1) • d Given the sequence 81, 80. 5, 80, 79. 5, 79, …, find the 9 th term.

Example 4: an = a 1 + (n – 1) • d Given the sequence 79, 75, 71, 67, 63, …, find the term number that is -169.

Example 5: an = a 1 + (n – 1) • d Suppose you are saving up for a new gaming system. You have 100 dollars this year, and you plan to add 33 dollars each of the following years. How much money will you have in 7 years?

Geometric Sequences An geometric sequence is defined as a sequence in which there is a common ratio between consecutive terms. Comm on Ratio = 2

Is the given sequence geometric? If so, identify the common ratio. 1. 2. 3. 4. 5. 5, 15, 45, 135, … 15, 30, 45, 60, … 6, -24, 96, -384, … 7, 0. 07, 0. 007, … 10, 4, 1. 6, 0. 64, …

Geometric Sequence Formula 1 st The number in the sequence. The same as the n in an. If you’re looking for the 5 th number in the sequence, n = 5. an = a 1 • r The “nth” number in the sequence. Ex. a 5 is the 5 th number in the sequence. (n-1) The common ratio.

Example 1: an = a 1 • r (n-1) Given the sequence 4, 28, 196, 1372, 9604, …, find the 14 th term.

Example 2: an = a 1 • r (n-1) Given the sequence -2, 6, -18, 54, -162, …, find the 17 th term.

Example 3: an = a 1 • r (n-1) Given the sequence 100, 83, 68. 89, 57. 1787, …, find the 9 th term.

Example 5: an = a 1 • r (n-1) Suppose you want a reduced copy of a photograph. The actual length of the photograph is 10 in. The smallest size the copier can make is 64% of the original. Find the length of the photograph after five reductions.