Question
what is the geometric sequence and 4th term for 2/95, -8/95, 32/95
Answers
Answered by
GPT 3.5
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.
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.