Download - AA Section 1-7a
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Section 1-7Explicit Formulas for Sequences
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In-Class Activity
See page 41.
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Term:
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Term:
Each figure, set of numbers, or value
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Term:
Each figure, set of numbers, or value
Explicit Formula for the nth Term:
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Term:
Each figure, set of numbers, or value
Explicit Formula for the nth Term:
Allows for us to find any term in a sequence
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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:
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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
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Example 1Use the formula we derived in the activity to find t15.
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Example 1Use the formula we derived in the activity to find t15.
tn= n(n +1), for int. n ≥1
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Example 1Use the formula we derived in the activity to find t15.
tn= n(n +1), for int. n ≥1
t15=15(15 +1)
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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)
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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
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Subscript/Index
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Subscript/Index
Tells us which term in the sequence that is being dealt with
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Subscript/Index
Tells us which term in the sequence that is being dealt with
t15 is the 15th term in the sequence
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Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
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Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1
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Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1 = 7 + 1
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Example 2
a. Find the first 4 terms. tn= 7n +1, for int. n ≥1.
t1 = 7(1) + 1 = 7 + 1 = 8
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Example 2
b. Find t12 and state what it means. tn= 7n +1, for int. n ≥1.
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Example 2
b. Find t12 and state what it means. tn= 7n +1, for int. n ≥1.
t12 = 7(12) + 1
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Example 2
b. Find t12 and state what it means. tn= 7n +1, for int. n ≥1.
t12 = 7(12) + 1 = 84 + 1
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Example 2
b. Find t12 and state what it means. tn= 7n +1, for int. n ≥1.
t12 = 7(12) + 1 = 84 + 1 = 85
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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
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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.
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Example 3a. Write an explicit formula for this situation
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Example 3a. Write an explicit formula for this situation
b
n= 80(.7)n
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Example 3a. Write an explicit formula for this situation
for all int. n ≥ 1 b
n= 80(.7)n
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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Example 3c. After how many bounces will the ball bounce less
than 9 feet?
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Example 3c. After how many bounces will the ball bounce less
than 9 feet?
b5 = 13.4456
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Example 3c. After how many bounces will the ball bounce less
than 9 feet?
b5 = 13.4456
b6 = 9.41192
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Example 3c. After how many bounces will the ball bounce less
than 9 feet?
b5 = 13.4456
b6 = 9.41192
b7 = 6.588344
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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
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Homework
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Homework
p. 45 #1-27