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