Example:
4, 7, 10, 13, 16, 19, 22
Use the following process to help find a formula for the pattern.
n: is the position or place value
tn: value of that position
When looking at the pattern this way, it is easy to see the it just adding three. So the formula would be.
tn= n-1+3
Or
tn=7n-9
Arithmetic Sequences:
(i) Recursive defintion: An order list of numbers generated by continnous adding value (the common)
(ii) Implictit defintin: An oredered list of numbers where each number n the list is generated by a linear equation.
Common Difference (d):
(i) The number that is repeatedly added to successive term in an arithemic sequence.
(ii) Fommr the implicit definitiion, d is the slope of the linear equation.
Recursivw: add to what you have. Ex: tn= tn-1+3
Explicit: a formula that uses the position or "n" value to find. Ex: tn= 3n+7
You should also know how to find the common difference
d = tn - t(n -
1)
d is the common difference
tn is an
arbitrary term in the sequence
t(n - 1) is
the term immediately before tn in the sequence
As well you should know how to find the nth term in an
arithmetic sequence
tn = a + (n -
1)d
tn is the nth
term
a is the first
term
n is the
"rank" of the nth term in the sequence
d is the
common difference
