Indicate whether the sequence is arithmetic, geometric, or neither.
6, 30, 150, 750, 3750, . . .
to be arithmetic, 30-6 = 150-30
to be geometric , 30/6 = 150/30
is either of those statements true?
If so, is the pattern true for all the numbers given?
To determine if the given sequence is arithmetic, geometric, or neither, we need to examine the pattern of the terms.
First, let's calculate the ratios between consecutive terms:
30 / 6 = 5
150 / 30 = 5
750 / 150 = 5
3750 / 750 = 5
Observing that the ratios are all the same (5), we can conclude that this is a geometric sequence.
In a geometric sequence, each term is obtained by multiplying the preceding term by a constant number called the common ratio. In this case, the common ratio is 5.
To verify this, let's calculate the next term:
3750 * 5 = 18,750
So, the next term in the sequence is 18,750.
Thus, the sequence 6, 30, 150, 750, 3750, . . . is a geometric sequence with a common ratio of 5.