Question

The explicit rule for a sequence is given. an=3n+1 What is the recursive rule for the sequence?

a1=4; an=an−1+1

a1=3; an=an−1+1

a1=1; an=an−1+3

a1=4; an=an−1+3

Answer 1

`a_1=4`

Recursive Rule:
`a_n=a_(n-1)+3`

D is correct

Explanation:

We are given explicit rule,

`a_n=3n+1`

Put n=1

`a_1=3(1)+1=4`

Now, we will find recursive rule

Put n=n-1

`a_(n-1)=3(n-1)+1`

`a_(n-1)=3n-2`

`a_n=3n+1`

Subtract the equation

`a_n-a_(n-1)=3n+1-3n+2`

`a_n-a_(n-1)=3`

`a_n=a_(n-1)+3`

Hence, The recursive rule is
`a_n=a_(n-1)+3`

Answer 2

a1 =4

an = an-1 +3

Explanation:

an = 3n+1

The common difference is the coefficient on the n term

d = 3

We will add 3 each time

an = an-1 +3

Let n =1

The 1st term is

a1 = 3(1) +1

a1 =4