Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively.

Step-by-step explanation:

The explicit form for a geometric sequence is where is the first term and is the common ratio.

We have the following given:

.

We also know that while .

So if we do 5th term divided by second term we get:

Simplifying both sides:

Cube root both sides:

The common ratio, r, is -3.

Now we need to find the first term.

That shouldn't be too hard here since we know the second term which is -21.

We know that first term times the common ratio will give us the second term.

So we are solving the equation:

.

Dividing both sides by -3 gives us .

So the equation is in it's explicit form is:

Check it!

Plugging in 2 should gives us a result of -21.

That checks out!

Plugging in 5 should give us a result of 567.

The checks out!

Our equation works!

step-by-step explanation:

what grade level is this? need to know so i can look in my old textbooks!

sure i'm up for it

step-by-step explanation: