Arithmetic Sequences.

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Presentation transcript:

Arithmetic Sequences

Arithmetic Sequence An arithmetic sequence is defined as a sequence in which there is a common difference between consecutive terms. Common Difference = 5

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

Arithmetic Sequence Formula The 1st number in the sequence. The common difference. an = a1 + (n – 1) • d The same as the n in an. If you’re looking for the 5th number in the sequence, n = 5. The “nth” number in the sequence. Ex. a5 is the 5th number in the sequence.

Example 1: an = a1 + (n – 1) • d Given the sequence -4, 5, 14, 23, 32, 41, 50,…, find the 14th term.

Example 3: an = a1 + (n – 1) • d Given the sequence 81, 80.5, 80, 79.5, 79,…, find the 9th term.

Example 4: an = a1 + (n – 1) • d Given the sequence 79, 75, 71, 67, 63,…, find the term number that is -169.

Example 5: an = a1 + (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

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

Is the given sequence geometric? If so, identify the common ratio. 5, 15, 45, 135, … 15, 30, 45, 60, … 6, -24, 96, -384, … 7, 0.7, 0.07, 0.007, … 10, 4, 1.6, 0.64, …

an = a1 • r (n-1) Geometric Sequence Formula The common ratio. The 1st number in the sequence. The same as the n in an. If you’re looking for the 5th number in the sequence, n = 5. an = a1 • r (n-1) The “nth” number in the sequence. Ex. a5 is the 5th number in the sequence. The common ratio.

Example 1: an = a1 • r (n-1) Given the sequence 4, 28, 196, 1372, 9604,…, find the 14th term.

Example 2: an = a1 • r (n-1) Given the sequence -2, 6, -18, 54, -162,…, find the 17th term.

Example 3: an = a1 • r (n-1) Given the sequence 100, 83, 68.89, 57.1787,…, find the 9th term.

Example 5: an = a1 • 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.