what is the 6th term of the geometric sequence 2000, 800, 320,..../
Start by taking the ratio of 800/2000
reduce it to 2/5 or .4
multiply 800 times .4 = 320
next multiply 320 times .4
and continue until you get to the 6th term.
you could do that, or just use the formula for the
nth term of a GS, which is ar^(n-1)
6th term = 2000(.4)^5 = 20.48
To find the 6th term of the geometric sequence, we need to determine the common ratio between the terms.
The common ratio (r) is found by dividing any term by its previous term. Let's take the second term (800) and divide it by the first term (2000):
800 ÷ 2000 = 0.4
So, the common ratio (r) is 0.4.
To find the 6th term, we can use the formula for the nth term of a geometric sequence:
a_n = a₁ * r^(n-1)
Where:
a_n is the nth term,
a₁ is the first term,
r is the common ratio, and
n is the position of the term we want to find.
Now, let's substitute the given values into the formula to find the 6th term:
a₆ = 2000 * 0.4^(6-1)
Simplifying:
a₆ = 2000 * 0.4^5
a₆ = 2000 * 0.4 * 0.4 * 0.4 * 0.4 * 0.4
Evaluating the expression:
a₆ ≈ 2000 * 0.01024
a₆ ≈ 20.48
Therefore, the 6th term of the geometric sequence 2000, 800, 320, ... is approximately 20.48.