Q:

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.

Accepted Solution

A:
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 differenceExplicit 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 numberSolution:  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