Question

what is the explicit formula and recursive formula of the numbers 4,7,10,13,16...i don't even know how to start this problem. i just need a bit of help or the answer because I'm running out of time.

Answer 1

An arithmetic sequence is a sequence with a constant

 increase or decrease also known as the constant difference

In the sequence 10, 40, 70, 100, ….

The constant difference between the terms is 30

A recursive formula for a sequence would be:

a1= first term in the sequence

an = term you are trying to find

an-1 = previous term in the sequence

d = constant difference

Explicit Formulas: 

A formula that allows you to find the nth term of the sequence by substituting known values in the expression.

Formula : an = a1 + d( n - 1)

a1= first term in the sequence

an = current term in the sequence

d = constant difference

n = term number

Solution: 

Write the explicit formula of the sequence 4, 7, 10, 13, 16 ….

Formula for explicit term:

an = ___ + ___( n - 1)

Simplify: an = ___ + ___n

In the sequence 4, 7, 10, 13, ….

To find the 11th term explicitly, I plug in the into the formula I just made: 

an = 1 + 3n

a11 = 1 + 3(11)   

a11 = 34 

Find the 15th term of the sequence using the formula: an = 1 + 3n

Write the recursive formula of the sequence 4, 7, 10, 13, ….

Recursive formula:

a1 =

an = a  n  - 1

In the sequence 4, 7, 10, 13, 16 ….

To find the 5th term recursively, I plug it into the formula I just made: 

  an = an-1 + 3

a5 = a5-1 + 3   in words: 5th  term equals the 4th term plus 3

a5 = 13 + 3 

a5 = 16  

Recursive and Explicit Formulas for Arithmetic (Linear) Sequences