1. Week 5
Warm Up
{ -3, 8, 19, 30, 41, . . }
n = 3
1) tn =
2) tn - 1 =
3) t6 =

2. Recursive Formula: Arithmetic
if a3 = 10
then a3 - 1 = 7
d = 3
Recursive Formula: Arithmetic
an = an
a50 =
a49 + 3

3. Geometry
Sequences Day 5
I will write an explicit formula for an arithmetic sequence of numbers.
Explicit Formula
You Do not need to know the previous number to find a number in the sequence.
an = dn + a0
Ex 1

4. Ex 2 • • • •

5. • • • • common difference? goes up by 3 common difference = slope Ex 2
output: , 7,
10,
13, • • •
input: 1, 2, 3, 4
common difference?
goes up by 3
common difference = slope

6. • • • • •
y = mx + b
Ex 3
y = x + 3 1
Explicit Formula
an = 3n + 1

7. • • • • • • an = 3n + 1 an = 3n + 1 a3 = 3(3) + 1 a50 = 3(50) + 1
Ex 4
a3 = 3(3) + 1
a50 = 3(50) + 1
a3 = 9 + 1
a50 =
a3 = 10
a50 = 151

8. a = { 10, 8, 6, 4, 2,. . .} y = -2x + 12 tn = -2n + 12 t0 = -2(0) + 12
Ex 5
y = -2x + 12
Term # n
Term tn 1 2 3 4 12
tn = -2n + 12 10
t0 = -2(0) + 12 8 6
t0 = 12 4
t0 = y-intercept

9. Explicit Formula: Arithmetic Sequence
an = dn + a0
-2, 7, 16, 25, . . .
Ex 6
d = 9
a0 = -11
an = 9n - 11

10. Handouts – 1.3 Day 1 Explicit Formulas
What is the explicit formula?
-6, 1, 8, 15, 22, . . .
Assignment:
Handouts – 1.3 Day 1 Explicit Formulas

11. a10
an = -2n + 12
a10 = -2( 10 ) + 12
a10 =
a10 = -8

12. • • • • • • an = 3n + 1 a0 = 3(0) + 1 a0 = 0 + 1 a0 = 1 Ex 5
a0 is the y-intercept
a0 = 1

13. You have to know the previous number to find the next number.
Recursive Formulas
You have to know the previous number to find the next number.
Arithmetic tn
tn – 1 d = +
Geometric
= r ( )
tn-1 tn