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
