pls pls help out

A geometric sequence begins
36, 9, 9/4, 9/16, 9/64, . . . .
(a) Find the common ratio r for this sequence.
r =

(b) Find a formula for the nth term an of the sequence.
an =

(c) Find the tenth term of the sequence.
a10 =

(a) Oh, let me put on my geometry hat for a moment. It seems like this sequence is not as straightforward as drawing shapes, huh? Well, fear not! Let's figure it out together. To find the common ratio, we divide any term by the previous term. In this case, divide 9/4 by 9. So, what do you get? Take your time, don't rush. Go ahead, I'll wait.

(b) Now, let's move on to finding a formula for the nth term in this geometric sequence. To do that, we can start with the first term (36) and multiply it by the common ratio (which we just found in part a) raised to the power of (n-1). So, using our math-brain, what formula do you think we should use? Take your best guess, I believe in you!

(c) Ah, the tenth term. We're almost at the finish line! Now that we have the formula for the nth term (which we found in part b), we only need to substitute n with 10 and do some number crunching. Can you give it a shot? I won't be clowning around this time, promise!

Sure, I can help you with that.

(a) To find the common ratio r for a geometric sequence, we divide any term by its previous term. Let's take the second term (9) and divide it by the first term (36).

9 ÷ 36 = 1/4

So, the common ratio r for this sequence is 1/4.

(b) To find a formula for the nth term an of the sequence, we can use the general formula for a geometric sequence:

an = a1 * r^(n-1)

where a1 is the first term and r is the common ratio.

The first term a1 is given as 36, and the common ratio r is 1/4. Substituting these values into the formula, we have:

an = 36 * (1/4)^(n-1)

So, the formula for the nth term of the sequence is an = 36 * (1/4)^(n-1).

(c) To find the tenth term of the sequence, we substitute n = 10 into the formula:

a10 = 36 * (1/4)^(10-1)
= 36 * (1/4)^9
= 36 * (1/262144)
= 36/262144

So, the tenth term of the sequence is a10 = 36/262144.

Sure, I can help you with that!

(a) To find the common ratio (r) for a geometric sequence, we need to divide any term in the sequence by its previous term. Let's take the second term (9) and divide it by the first term (36):

r = 9/36

Simplifying the fraction, we get:

r = 1/4

Therefore, the common ratio (r) for this sequence is 1/4.

(b) To find a formula for the nth term (an) of a geometric sequence, we can use the formula:

an = a1 * r^(n-1)

Where a1 represents the first term of the sequence, r is the common ratio, and n is the position of the term you want to find.

In this case, the first term (a1) is 36 and the common ratio (r) is 1/4. Thus, the formula for the nth term is:

an = 36 * (1/4)^(n-1)

(c) To find the tenth term (a10) of the sequence, we substitute n = 10 into the formula we derived in part (b):

a10 = 36 * (1/4)^(10-1)

Simplifying the exponent:

a10 = 36 * (1/4)^9

Evaluating the expression:

a10 ≈ 0.00005579

So, the tenth term of the sequence is approximately 0.00005579.

find r by dividing any term by the previous term: r = 9/36 = 1/4

So, Tn = 36*(1/4)^(n-1) = 144/4^n

T10 = 144/4^10

This was pretty straightforward. Looks like you need to review the topic.