Answer:
Tn = -4^n/2
Explanation:
The formula for nth tern of a geometric sequence is given as:
Tn = ar^n-1 where;
a is the first term
r is the common ratio
n is the number of terms
Since we are looking for the nth term if the geometric sequence, we will write our answer as a function if 'n'.
Given the second and fifth terms to be -8 and 512, respectively, this can be interpreted as;
T2 = ar^2-1 = -8
T5 = ar^5-1 = 512
From the equations above, we have;
ar = -8... (1)
ar⁴ = 512
Dividing both equation, we have;
ar⁴/ar = -512/8
r³ = -64
r = -4
Substituting r = -4 into equation 1, we have;
a(-4) = -8
-4a = -8
a = 2
Since nth term Tn = ar^n-1
Substituting the value of a and r into the equation will give;
Tn = 2(-4)^n-1
2(-4^n × -4^-1)
2(-4^n × -1/4)
= -4^n/2