Arithmetic and Geometric Sequences 5.7 Arithmetic and Geometric Sequences

Sequences A sequence is a list of numbers that are related to each other by a rule. The terms are the numbers that form the sequence.

Arithmetic Sequence An arithmetic sequence is a sequence in which each term after the first term differs from the preceding term by a constant amount. The common difference, d, is the amount by which each pair of successive terms differs. To find the difference, simply subtract any term from the term that directly follows it.

General Term of an Arithmetic Sequence Find the 5th term of the arithmetic sequence whose first term is 4 and whose common difference is 8. an = a1 + (n  1)(d) a5 = 4 + (5  1)(8) = 4 + (4)(8) = 4 + (32) = 28

Sum of the First n Terms in an Arithmetic Sequence Find the sum of the first 50 terms in the arithmetic sequence: 2, 4, 6, 8,…100

Geometric Sequences A geometric sequence is one in which the ratio of any term to the term that directly precedes it is a constant. This constant is called the common ratio, r. r can be found by taking any term except the first and dividing it by the preceding term.

General Term of a Geometric Sequence Find the 6th term for the geometric sequence with the first term = 3 and the common ratio = 4.

Sum of the First n Terms in an Geometric Sequence

Example Find the sum of the first 4 terms of the geometric sequence for r = 2 and the first term = 3.

Homework P. 275 # 9 – 69 (x3)