Arithmetic and Geometric Sequences!

*Sequence-a list of numbers. Two types of sequences:
--Arithmetic sequence-made by adding the same positive or negative interger to generate the sequence
-Fromula tn=t1=(n-1) d
-t1=first term
-n=term #
-d=difference (what is being added or subtracted)
-tn=last term

--Geometric sequence-made by mulitiplying by the same whole number or fraction to generate a sequence.
-Fromula tn=t1 * r ^(n-1)
-r=ratio the number that is mulitiplied to generate the sequence
-t1=first term
-n=term # (tn= ___ term)

There are many ways to generate a sequence using these formulas or to find the formula for a sequence of numbers.

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Ex.1:
Find a formula for tn.
1, 4, 7, 10, ...
d=3
t1=1
n=n
tn=t1+(n-1)d
1+(n-1)3
=1+3n-3
tn=3n-4

Ex.2: Is the following sequence arithmitic or geometric? Find the formula for the nth term.
3,5,7,9,11...

This would be arithmitic because we are adding 2. Therefore d = 2. To find the formula for the nth term we need to plug numbers into the formula:
tn = t1 + (n-1)d
tn = 3 + (n-1)2
tn = 3 + 2n - 2
tn=2n+1