A). Find the explicit expression for this sequence
Ans: A(n)=3n-2
B. Find the recursive expression for this sequence
Ans: A(n)=A(n-1)+3
C. What is the 15th term?
Ans: 15th term is 43
Explanation:
Arithmetic sequence is given by a,a+d,a+2d,a+3d.......a+(n-1)d
Where a is first term of arithmetic sequence
Let,
The coordinates of x axis represent the location of term, say n
The coordinates of y axis represent the value of pespective term
We can write
Arithmetic sequence as 1,4,7...........
Where a=1 and a+d=4
For value of d,
d=(a+d)-(a)=(4)-(1)=3
A. Find the explicit expression for this sequence
Ans:
Explicit expression is given by A(n)=a+(n-1)d
For given Arithmetic sequence as 1,4,7...........
Explicit expression will be
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:
Recursive expression is given by A(n)=A(n-1)+d
For given Arithmetic sequence as 1,4,7...........
Recursive expression will be
A(n)=A(n-1)+d
A(n)=A(n-1)+3
C. What is the 15th term?
Ans:
For given Arithmetic sequence as 1,4,7...........
Explicit expression is given by
A(n)=3n-2
For 15th term n=15
A(n)=3(15)-2=45-2=43
Thus, 15th term is 43