Welcome Is the number 27 a term in the sequence represented by the explicit formula an = 4n – 1? Is the number 97 a term in the sequence represented by the explicit formula an = 4n – 1?

HW Key (half-sheet) 1, 4, 7, 10, 13 14, 12, 10, 8, 6 a8 = 19; an = 2n + 3 a1 = -34.5 an = an-1 + 4.5, n > 1 a8 = y – 17 an = -3n + y + 7

Objectives and HW The students will be able to identify geometric sequences and write them in explicit and recursive form. HW: p. 788: 2,6,8,14,18 (Write both explicit and recursive formulas!!!)

Definition of Terms Geometric Sequence – (or geometric progression) is a sequence in which terms are found by multiplying a preceding term by a nonzero constant. The common ratio is denoted by r .

Recursive Formula for the nth term of a Geometric Sequence: In a geometric sequence: a1 = # an = r·an-1 where r = common ratio r =

Example 1: If the sequence is geometric, find the common ratio and give the recursive formula : 2, 8, 14, 20, . . . 72, 36, 18, . . . 2, 6, 18, 54, . . .

Explicit Formula for the nth term of a Geometric Sequence: In a geometric sequence {an} an = a1(r)n-1 where r = common ratio.

Explicit Form of a Geometric Sequence Ex 2: Given the explicit formula, find the common ratio r and the first term u1 : a) b) c)

Explicit Form of a Geometric Sequence Ex 3: Write the explicit form of a geometric sequence where the first two terms are 8 and –2 respectively. Then find the first 5 terms. To find the common ratio r: explicit formula The 1st 5 terms:

Explicit Form of a Geometric Sequence Ex 4: Find the explicit form of the geometric sequence given that u2 = 6 and u7 = 192. To find the common ratio r: