Find an equation for the nth term of a geometric sequence where the second and fifth terms or -8 and 512, respectively

Tn = -4^n/2

Step-by-step 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

step-by-step :

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step-by-step explanation: