Write a recursive formula for the sequence 7, 13, 19, 25, 31 then find the next term in the sequence?

The recursive formula is

and the next term is in the sequence is 37.

Step-by-step explanation:

We first have to find a pattern in the numbers we are given. We notice that each number is 6 greater than the previous; for example 13 is 7+6, 19 is 13+6 and so on. Mathematically we write this as

Where is the value of nth term of the sequence.

The sequence starts at 7, therefore the first term in the sequence is:

Now the next term (it will be 6th term) of the sequence will be 6 greater than the previous term, and since the previous term is 31, we have:

.

Thus the next term in the sequence is 37, and the recursive formula is

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>