Answer:
A). Explicit expression is given by A(n)=3n-2.
B). The recursive expression is given by A(n)=A(n-1)+3
C). 15th term is 43.
Explanation:
Given graph represent the arithmetic sequence
where, x axis show position of term and y-axis show value of respective position.
The arithmetic sequence is given by a,a+d,a+2d......a+(n-1)d
Here, The arithmetic sequence is written as 1,4,7....
On comparing both arithmetic sequence,
a=1 and a+d=4
Therefore, d=4-a=4-1=3
A. Find the explicit expression for this sequence
Ans.
Explicit expression is given by A(n)=a+(n-1)d
A(n)=a+(n-1)d.
A(n)=1+(n-1)3
A(n)=1+3n-3
A(n)=3n-2.
B. Find the recursive expression for this sequence
Ans.
The recursive expression is given by A(n)=A(n-1)+d
A(n)=A(n-1)+d
A(n)=A(n-1)+3
Where, A(n-1)=3(n-1)-2
A(n-1)=3n-3-2
A(n-1)=3n-5
C. What is the 15th term?
Ans.
By using explicit expression for this sequence
A(n)=3n-2.
A(15)=3(15)-2
A(15)=45-2=43
Thus, 15th term is 43.