Asked by Juanita Courtney on Mar 10, 2024
Verified
Write the first five terms of the arithmetic sequence defined recursively. a1=12,ak+1=ak+6a _ { 1 } = 12 , a _ { k + 1 } = a _ { k } + 6a1=12,ak+1=ak+6
A) a1=18,a2=30,a3=42,a4=54,a5=66a _ { 1 } = 18 , a _ { 2 } = 30 , a _ { 3 } = 42 , a _ { 4 } = 54 , a _ { 5 } = 66a1=18,a2=30,a3=42,a4=54,a5=66
B) a1=12,a2=24,a3=36,a4=48,a5=60a _ { 1 } = 12 , a _ { 2 } = 24 , a _ { 3 } = 36 , a _ { 4 } = 48 , a _ { 5 } = 60a1=12,a2=24,a3=36,a4=48,a5=60
C) a1=12,a2=24,a3=18,a4=36,a5=30a _ { 1 } = 12 , a _ { 2 } = 24 , a _ { 3 } = 18 , a _ { 4 } = 36 , a _ { 5 } = 30a1=12,a2=24,a3=18,a4=36,a5=30
D) a1=18,a2=24,a3=30,a4=36,a5=42a _ { 1 } = 18 , a _ { 2 } = 24 , a _ { 3 } = 30 , a _ { 4 } = 36 , a _ { 5 } = 42a1=18,a2=24,a3=30,a4=36,a5=42
E) a1=12,a2=18,a3=24,a4=30,a5=36a _ { 1 } = 12 , a _ { 2 } = 18 , a _ { 3 } = 24 , a _ { 4 } = 30 , a _ { 5 } = 36a1=12,a2=18,a3=24,a4=30,a5=36
Arithmetic Sequence
A sequence of numbers in which each term after the first is obtained by adding a constant difference to the preceding term.
Recursive Definition
A definition of a function, sequence, or process in which the next term is defined in terms of previous terms.
- Assess and assign sequences as either arithmetic or geometric.
- Translate recursive sequence definitions into explicit formulas.
Verified Answer
MH
Mohamed HanafyMar 10, 2024
Final Answer :
E
Explanation :
Using the given recursive formula, we can generate the terms of the sequence:
a1=12a_1=12a1=12
a2=a1+6=18a_2=a_1+6=18a2=a1+6=18
a3=a2+6=24a_3=a_2+6=24a3=a2+6=24
a4=a3+6=30a_4=a_3+6=30a4=a3+6=30
a5=a4+6=36a_5=a_4+6=36a5=a4+6=36
Therefore, the correct answer is choice E.
a1=12a_1=12a1=12
a2=a1+6=18a_2=a_1+6=18a2=a1+6=18
a3=a2+6=24a_3=a_2+6=24a3=a2+6=24
a4=a3+6=30a_4=a_3+6=30a4=a3+6=30
a5=a4+6=36a_5=a_4+6=36a5=a4+6=36
Therefore, the correct answer is choice E.
Learning Objectives
- Assess and assign sequences as either arithmetic or geometric.
- Translate recursive sequence definitions into explicit formulas.