Hullo! So my question is: Can a geometric sequence have division?
For example, would this sequence be geometric because I could divide by two:
4, 2, 1, 0.5, etc.
sure -- r = 1/2
division is just multiplication by a fraction.
Thank you!
Hello! To determine whether a sequence is geometric, you need to check if there is a common ratio between each term. In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio.
In the sequence you provided, 4, 2, 1, 0.5, etc., you are dividing each term by 2 to obtain the next term. While this is a consistent operation, it does not follow the definition of a geometric sequence.
Geometric sequences involve multiplication rather than division. In a geometric sequence, the ratio between two consecutive terms remains constant throughout the sequence. For example, if you were to divide the terms in the sequence you provided by 2, you would have 2, 1, 0.5, 0.25, etc., which is a geometric sequence with a common ratio of 0.5.
To determine if a sequence is geometric, look for a consistent multiplication or division operation between terms.