Question
Find the 8th term of the geometric sequence 4, -20, 100,...
Answers
GPT 3.5
To find the 8th term of a geometric sequence, we can use the formula for the nth term of a geometric sequence:
a_n = a_1 * r^(n-1)
where:
a_n is the nth term
a_1 is the first term
r is the common ratio
n is the term number
In this case:
a_1 = 4
r = -5 (-20 / 4)
n = 8
Plugging in the values:
a_8 = 4 * (-5)^(8-1)
a_8 = 4 * (-5)^7
a_8 = 4 * -78125
a_8 = - 312500
Therefore, the 8th term of the geometric sequence 4, -20, 100,... is -312500.
a_n = a_1 * r^(n-1)
where:
a_n is the nth term
a_1 is the first term
r is the common ratio
n is the term number
In this case:
a_1 = 4
r = -5 (-20 / 4)
n = 8
Plugging in the values:
a_8 = 4 * (-5)^(8-1)
a_8 = 4 * (-5)^7
a_8 = 4 * -78125
a_8 = - 312500
Therefore, the 8th term of the geometric sequence 4, -20, 100,... is -312500.