Write the explicit formula for the geometric sequence.
8,6,4 1/2, 3 3/8
What is the explicit formula for the given geometric sequence?
An=.................
well,
a = 8
r = 3/4
Tn = 8 * (3/4)^(n-1)
To find the explicit formula for a geometric sequence, we need to determine the common ratio (r). The common ratio between any two consecutive terms in a geometric sequence is found by dividing the second term by the first term, the third term by the second term, and so on.
For example, in the given sequence: 8, 6, 4 1/2, 3 3/8
The common ratio between 6 and 8 is 6/8 or 3/4.
The common ratio between 4 1/2 and 6 is also 3/4.
Thus, we can conclude that the common ratio (r) for this sequence is 3/4.
Now, to find the explicit formula for a geometric sequence, we use the formula:
An = A1 * r^(n-1)
where:
- An represents the nth term of the sequence
- A1 is the first term of the sequence
- r is the common ratio
- n is the position of the term in the sequence that we're looking for
Substituting the given values in our case, A1 is 8, and r is 3/4, our formula becomes:
An = 8 * (3/4)^(n-1)
Therefore, the explicit formula for the given sequence is:
An = 8 * (3/4)^(n-1)