Create an image of a geometric progression depicted visually. There should be exactly seven circles arranged in a row, each representing a term in the sequence. The first circle should be filled up to represent the value of 16, and the fifth circle should be filled up to represent the value of 9. The other circles should illustrate the shrinking pattern between the values, but their exact values are not specified. The image presents a visual aid to conceptualize the 7th term of the geometric progression. The image should not contain any text.

find the 7th term of the geometric progression if the first and 5th terms are 16 and 9 respectively.

a = 16

ar^4 = 9
sub in a = 16
16r^4 = 9
4r = ± 3
r = ± 3/4

7th term = ar^6
= 16(±3/4) = 16(729/4096)
= 729/256

I don't understand

I dont understand

Why did the geometric progression go to therapy? Because it wanted to find its seventh term and needed a little extra help!

To find the 7th term of a geometric progression, we need to find the common ratio first. The common ratio (r) can be found by dividing any term by its previous term.

In this case, we have the first term (a₁) as 16 and the 5th term (a₅) as 9.

So, the common ratio (r) is found by dividing the 5th term by the first term: r = a₅ / a₁ = 9 / 16.

Now that we have the common ratio, we can find the 7th term (a₇) using the formula:

a₇ = a₁ * r^(n-1), where n is the term number we're looking for.

Plugging in the values, we have:
a₇ = 16 * (9 / 16)^(7-1)
= 16 * (9 / 16)^6

Calculating it, we get:
a₇ ≈ 5.0625

So, according to my calculations, the 7th term of the geometric progression is approximately 5.0625. Hope that brings a smile to your face!

To find the 7th term of a geometric progression, we need to find the common ratio (r) first.

The formula for the nth term (Tn) of a geometric progression is:
Tn = a * r^(n-1),
where a is the first term, r is the common ratio, and n is the term number.

We are given that the first term (a) is 16 and the fifth term (T5) is 9.

We can use this information to find the common ratio (r). Let's substitute the values into the formula to solve for r:
T5 = a * r^(5-1)
9 = 16 * r^4

Now we can solve this equation for r. Divide both sides by 16:
r^4 = 9/16

To isolate r, we take the fourth root of both sides:
r = (9/16)^(1/4)

Now, we can use the common ratio (r) to find the seventh term (T7). Let's substitute the values into the formula:
T7 = a * r^(7-1)
T7 = 16 * r^6

Substitute the value of r that we found:
T7 = 16 * [(9/16)^(1/4)]^6

Now, we can simplify this expression to find the 7th term.