Find the explicit formula for the general nth term of the geometric sequence described below.

a4= -32 and a7= -256

an=?

Step-by-step explanation:

Let the geometric sequence be:

First term:

Second term:

Third term:

Fourth term:  

Follow the pattern for the terms between the 4th and 7th: ..........

Seventh term:

Follow the pattern for the terms between the 7th and the nth: .........

So we need to find which the value of the first term.

We need to find which is the common ratio here.

So if we take the 7th term and divide the 4th term we get the following equation:

Now the first thing I notice is on the left hand side. I can cancel out some common factors over the numerator and denominator:

Now I see to find the common ratio, , we can just take the cube root of both sides:

is true since 2(2)(2)=8.

So after finding has value 2, we need to find which is the first term of the sequence.

Let's use one of our equations with a given value for it:

with :

Divide both sides by 8:

So the first term,, has value -4.

So the explicit form of this geometric sequence is:

Let's verify:

What happens when ?

That look's good.

Let's check the other given condition.

?

Since both of the conditions are satisfied, we have done our job and it is confirmed.

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.

multiply then divide

step-by-step explanation: