aa section 1-7a
TRANSCRIPT
Section 1-7Explicit Formulas for Sequences
In-Class Activity
See page 41.
Term:
Term:
Each figure, set of numbers, or value
Term:
Each figure, set of numbers, or value
Explicit Formula for the nth Term:
Term:
Each figure, set of numbers, or value
Explicit Formula for the nth Term:
Allows for us to find any term in a sequence
Term:
Each figure, set of numbers, or value
Explicit Formula for the nth Term:
Allows for us to find any term in a sequence
Sequence:
Term:
Each figure, set of numbers, or value
Explicit Formula for the nth Term:
Allows for us to find any term in a sequence
Sequence:
A function whose domain is the natural numbers
Example 1Use the formula we derived in the activity to find t15.
Example 1Use the formula we derived in the activity to find t15.
tn= n(n +1), for int. n ≥1
Example 1Use the formula we derived in the activity to find t15.
tn= n(n +1), for int. n ≥1
t15=15(15 +1)
Example 1Use the formula we derived in the activity to find t15.
tn= n(n +1), for int. n ≥1
t15=15(15 +1)
=15(16)
Example 1Use the formula we derived in the activity to find t15.
tn= n(n +1), for int. n ≥1
t15=15(15 +1)
=15(16)
= 240
Subscript/Index
Subscript/Index
Tells us which term in the sequence that is being dealt with
Subscript/Index
Tells us which term in the sequence that is being dealt with
t15 is the 15th term in the sequence
Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1
Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1 = 7 + 1
Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1 = 7 + 1 = 8
Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1 = 7 + 1 = 8
t2 = 7(2) + 1
Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1 = 7 + 1 = 8
t2 = 7(2) + 1 = 14 + 1
Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1 = 7 + 1 = 8
t2 = 7(2) + 1 = 14 + 1 = 15
Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1 = 7 + 1 = 8
t2 = 7(2) + 1 = 14 + 1 = 15
t3 = 7(3) + 1
Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1 = 7 + 1 = 8
t2 = 7(2) + 1 = 14 + 1 = 15
t3 = 7(3) + 1 = 21 + 1
Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1 = 7 + 1 = 8
t2 = 7(2) + 1 = 14 + 1 = 15
t3 = 7(3) + 1 = 21 + 1 = 22
Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1 = 7 + 1 = 8
t2 = 7(2) + 1 = 14 + 1 = 15
t3 = 7(3) + 1 = 21 + 1 = 22
t4 = 7(4) + 1
Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1 = 7 + 1 = 8
t2 = 7(2) + 1 = 14 + 1 = 15
t3 = 7(3) + 1 = 21 + 1 = 22
t4 = 7(4) + 1 = 28 + 1
Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1 = 7 + 1 = 8
t2 = 7(2) + 1 = 14 + 1 = 15
t3 = 7(3) + 1 = 21 + 1 = 22
t4 = 7(4) + 1 = 28 + 1 = 29
Example 2
b. Find t12 and state what it means. tn= 7n +1, for int. n ≥1.
Example 2
b. Find t12 and state what it means. tn= 7n +1, for int. n ≥1.
t12 = 7(12) + 1
Example 2
b. Find t12 and state what it means. tn= 7n +1, for int. n ≥1.
t12 = 7(12) + 1 = 84 + 1
Example 2
b. Find t12 and state what it means. tn= 7n +1, for int. n ≥1.
t12 = 7(12) + 1 = 84 + 1 = 85
Example 2
b. Find t12 and state what it means.
The twelfth term of the sequence is 85.
tn= 7n +1, for int. n ≥1.
t12 = 7(12) + 1 = 84 + 1 = 85
Example 3
Matt Mitarnowski is standing on the top of an 80 foot-high wall. Don’t ask me why he’s up there. He’s weird like that. But while he’s up there, he
decided to drop a ball, which will bounce back 70% of its previous height.
Example 3a. Write an explicit formula for this situation
Example 3a. Write an explicit formula for this situation
b
n= 80(.7)n
Example 3a. Write an explicit formula for this situation
for all int. n ≥ 1 b
n= 80(.7)n
Example 3a. Write an explicit formula for this situation
for all int. n ≥ 1
b. Write the first four terms of this sequence b
n= 80(.7)n
Example 3a. Write an explicit formula for this situation
for all int. n ≥ 1
b. Write the first four terms of this sequence b
n= 80(.7)n
b
1= 80(.7)1
Example 3a. Write an explicit formula for this situation
for all int. n ≥ 1
b. Write the first four terms of this sequence b
n= 80(.7)n
b
1= 80(.7)1 = 56
Example 3a. Write an explicit formula for this situation
for all int. n ≥ 1
b. Write the first four terms of this sequence b
n= 80(.7)n
b
1= 80(.7)1 = 56
b
2= 80(.7)2
Example 3a. Write an explicit formula for this situation
for all int. n ≥ 1
b. Write the first four terms of this sequence b
n= 80(.7)n
b
1= 80(.7)1 = 56
b
2= 80(.7)2
= 39.2
Example 3a. Write an explicit formula for this situation
for all int. n ≥ 1
b. Write the first four terms of this sequence b
n= 80(.7)n
b
1= 80(.7)1 = 56
b
2= 80(.7)2
= 39.2
b
3= 80(.7)3
Example 3a. Write an explicit formula for this situation
for all int. n ≥ 1
b. Write the first four terms of this sequence b
n= 80(.7)n
b
1= 80(.7)1 = 56
b
2= 80(.7)2
= 39.2
b
3= 80(.7)3
= 27.44
Example 3a. Write an explicit formula for this situation
for all int. n ≥ 1
b. Write the first four terms of this sequence b
n= 80(.7)n
b
1= 80(.7)1 = 56
b
2= 80(.7)2
= 39.2
b
3= 80(.7)3
= 27.44
b
4= 80(.7)4
Example 3a. Write an explicit formula for this situation
for all int. n ≥ 1
b. Write the first four terms of this sequence b
n= 80(.7)n
b
1= 80(.7)1 = 56
b
2= 80(.7)2
= 39.2
b
3= 80(.7)3
= 27.44
b
4= 80(.7)4
=19.208
Example 3a. Write an explicit formula for this situation
for all int. n ≥ 1
b. Write the first four terms of this sequence b
n= 80(.7)n
b
1= 80(.7)1 = 56
b
2= 80(.7)2
= 39.2
b
3= 80(.7)3
= 27.44
b
4= 80(.7)4
=19.208
Don’t forget the labels! All answers are in feet.
Example 3c. After how many bounces will the ball bounce less
than 9 feet?
Example 3c. After how many bounces will the ball bounce less
than 9 feet?
b5 = 13.4456
Example 3c. After how many bounces will the ball bounce less
than 9 feet?
b5 = 13.4456
b6 = 9.41192
Example 3c. After how many bounces will the ball bounce less
than 9 feet?
b5 = 13.4456
b6 = 9.41192
b7 = 6.588344
Example 3c. After how many bounces will the ball bounce less
than 9 feet?
It will take 7 bounces until the ball bounces less than 9 feet.
b5 = 13.4456
b6 = 9.41192
b7 = 6.588344
Homework
Homework
p. 45 #1-27