given the recursive rule R(n)=R(n-1)+2, R(1)=2. what are the first five terms of the sequence

Question

Also, is the problem linear or nonlinear

 

Answer 1

Luckily, they gave use the first term in the sequence, R(1)=2

 

So lets apply the rule R(n)=R(n-1)+2 to generate the next four terms,

 

R(2)=R(2-1)+2=R(1)+2=2+2=4

R(3)=R(2)+2=4+2=6

R(4)=R(3)+2=6+2=8

R(5)=R(4)+2=8+2=10

 

There are your first 5 terms: 2,4,6,8,10

 

Note you can find each term in the sequence by multiplying the term sequence number, n, by 2.  Meaning you can rewrite the rule for the sequence non recursively as

 

R(n)=2n

 

This looks a lot like f(x)=2x, which looks a lot like y=2x, which is the equation of a line. 

 

Hence the rule is linear.

 

Good Luck

 

Cheers

 

-Chris