what is the rule for the geometric sequence: 5000, 500, 50, 5?
how about
term(n) = 5000/10^(n-1) or 5000(10)^(1-n)
To determine the rule for the given geometric sequence: 5000, 500, 50, 5, we need to observe the pattern and find the common ratio between consecutive terms.
In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio (r). Therefore, to find the common ratio, we can divide any term by its previous term.
Let's calculate the common ratio between each term:
- The common ratio between 500 and 5000 is 5000/500 = 10.
- The common ratio between 50 and 500 is 500/50 = 10.
- The common ratio between 5 and 50 is 50/5 = 10.
Since the common ratio is the same (10) for each term, we can conclude that the rule for this geometric sequence is multiplying each term by 10 to get the next term. Therefore, the rule for this sequence is:
The nth term (term at position n) is given by: a_n = a * r^(n-1).
In this case, the first term (a) is 5000, and the common ratio (r) is 10. So, the rule for this geometric sequence is:
a_n = 5000 * 10^(n-1), where n is the position of the term in the sequence.