what is the geometric sequence and 4th term for 2/95, -8/95, 32/95
A geometric sequence is a sequence in which each term after the first is found by multiplying the preceding term by a fixed, non-zero number called the common ratio.
In the given sequence, we can find the common ratio by dividing any term by its previous term. Let's take the second term (-8/95) divided by the first term (2/95):
(-8/95)/(2/95) = -8/2 = -4
Therefore, the common ratio for this geometric sequence is -4.
To find the fourth term, we can use the formula for the nth term of a geometric sequence:
a_n = a_1 * r^(n-1)
where a_n represents the nth term, a_1 is the first term, r is the common ratio, and n is the position of the term we want to find.
In this case, we know that a_1 = 2/95, r = -4, and n = 4:
a_4 = (2/95) * (-4)^(4-1)
Simplifying, we get:
a_4 = (2/95) * (-4)^3
= (2/95) * (-64)
= -128/95
Therefore, the fourth term of the geometric sequence 2/95, -8/95, 32/95 is -128/95.
To find the fourth term of a geometric sequence, we need to determine the common ratio (r) first.
In a geometric sequence, each term is obtained by multiplying the previous term by the common ratio. To find the common ratio, we can divide any term by its previous term.
Let's use the given terms:
-8/95 ÷ 2/95 = (-8/95) × (95/2) = -8/2 = -4
The common ratio (r) is -4.
Now, we can use the formula for the nth term of a geometric sequence:
An = A1 * r^(n-1)
Here, A1 is the first term, r is the common ratio, and n is the term number.
We are looking for the fourth term (n = 4), given A1 = 2/95 and r = -4:
A4 = (2/95) * (-4)^(4-1)
= (2/95) * (-4)^3
= (2/95) * (-64)
= -128/95
Therefore, the fourth term of the geometric sequence is -128/95.