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 Name__________________________________________ Date____________ Per_____ 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
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