Question

give a recursive formula for the sequence 1, 4, 7, 10, 13, 16

Answer 1

We are given the sequence:

1, 4, 7, 10, 13, 16

This is an arithmetic sequence since there is a common difference between each term. In this case, adding  3 to the previous term in the sequence gives the next term.

This is the  formula for arithmetic sequence :

$a_{n}=a_{1}+d(n-1)$

Now we have our first term a₁ = 1

common difference d=3

So plugging these values in the formula we have,

$a_{n}=1+3(n-1)$

$a_{n}=1+3n-3$

The final formula is :

$a_{n}=3n-2$

Answer 2

Answer:

We are given the sequence:

1, 4, 7, 10, 13, 16

This is an arithmetic sequence since there is a common difference between each term. In this case, adding  3 to the previous term in the sequence gives the next term.

This is the  formula for arithmetic sequence :

a_{n}=a_{1}+d(n-1)an=a1+d(n−1)

Now we have our first term a₁ = 1

common difference d=3

So plugging these values in the formula we have,

a_{n}=1+3(n-1)an=1+3(n−1)

a_{n}=1+3n-3an=1+3n−3

The final formula is :

a_{n}=3n-2an=3n−2