1. 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?

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

3. 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!!!)

4. 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 .

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

6. 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, . . .

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

8. 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)

9. 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:

10. 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: