Recursive and Explicit Formulas Day 1 Arithmetic WS SOLUTIONS

Recursive and Explicit Formulas Day 1 Arithmetic WS SOLUTIONS
a1
term
a2
a3
a4
a5
an
a45
a500
# of skeletons
First, fill in the first 4 terms.
What is the initial condition?
Is this sequence arithmetic or geometric or neither?
Is there a common difference or common ratio? If so, what is it?
Fill in the 5th term.
"Add one to the previous term" "The nth term is equal to the previous term plus one" an = a(n­1) + 1
Recursive Rule in WORDS
Pull
Recursive
Formula
Pull
Explicit Rule in WORDS
Pull
Explicit
Formula
"Multiply one by the number of steps of the sequence and add two, because that's where we started." "The nth term is equal to two plus one times the number of steps" an = 2 + (n­1)1
Pull
Now go back and calculate the 45th and 500th terms!
.
Recursive and Explicit Formulas Day 1 Arithmetic WS SOLUTIONS
term
a1
a2
a3
a4
a5
an
a20
# of cats
First, fill in the first 3 terms.
What is the initial condition?
Is this sequence arithmetic or geometric or neither?
Is there a common difference or common ratio? If so, what is it?
Fill in terms 4 and 5.
"Subtract three from the previous term" "The nth term is equal to the previous term minus three" an = a(n­1) + (­3)
Recursive Rule in WORDS
Pull
Recursive
Formula
Pull
Explicit Rule in WORDS
Pull
Explicit
Formula
"Multiply negative 3 by the number of steps of the sequence and add seven, because that's where we started." "The nth term is equal to seven plus negative three times the number of steps" an = 7 + (n­1)(­3)
Pull
Now go back and calculate the 20th and 100th terms!
.
a100
Recursive and Explicit Formulas Day 1 Arithmetic WS SOLUTIONS
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Writing Recursive and Explicit Formulas #1
Fill in the table for each picture pattern. State the initial condition, recursive and explicit formulas.
1.
term
# of leaves
a1
a2
a3
a4
3 5 7 9
+2
a. What is the initial condition?
b. Recursive Formula:
c. Explicit Formula:
an = a(n­1) + 2
an = 3 + (n­1)2
an
a25
51
an = 3 + (25­1)2
Recursive and Explicit Formulas Day 1 Arithmetic WS SOLUTIONS
2.
term
# of acorns
a4
a1
a2
1
6 11 16
a3
an
a17
81
+5
a. What is the initial condition?
b. Recursive Formula:
c. Explicit Formula:
an = a(n­1) + 5
an = 1 + (n­1)5
an = 1 + (17­1)5