Goemetric sequence :
A sequence is a goemetric sequence if an/an-1is the same non-zero number for all natural numbers greater than 1.
Arithmetic sequence :
A sequence {an} is an arithmetic sequence if an-an-1 is the same number for all natural numbers greater than 1.
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The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers".
To check whether it is an arithmetic sequence, verify whether the difference between two consecutive numbers is always the same.To check whether it is a geometric sequence, verify whether the ratio between two consecutive numbers is always the same.
It is an arithmetic sequence if you can establish that the difference between any term in the sequence and the one before it has a constant value.
The sequence is arithmetic if the difference between every two consecutive terms is always the same.
what is the recursive formula for this geometric sequence?