The 23rd term in a certain geometric sequence is 16 and the 28th term in the sequence is 24. What is the 43rd term?

It is not 48.

a+22d = 16

a+27d = 24

a = -96/5
d = 8/5

-96/5 + 42*8/5 = -96/5 + 336/5 = 240/5 = 48

If 48 is marked wrong, the key is in error. You could have checked it yourself.

This is what you did wrong, i think. YOu multiply not add.

Or, look at it this way. From T23 to T28 is 5 terms, and the value grew by 8.

From T28 to T43 is 15 terms = 3*5, so the value will grow by 3*8, or 24.

24+24 = 48

To find the 43rd term in the geometric sequence, we need to determine the common ratio (r) of the sequence using the given information.

Let's use the formulas for finding the nth term of a geometric sequence:

For any term in a geometric sequence, we can use the formula:

an = a1 * r^(n-1)

Where:
an is the nth term
a1 is the first term
r is the common ratio
n is the term number

We are given the values of the 23rd term (an = 16) and the 28th term (an = 24).

Using the formula, we can set up the following equations:

16 = a1 * r^(23-1)
24 = a1 * r^(28-1)

Now, divide these two equations:
(16/24) = r^(23-1) / r^(28-1)

Simplifying further:
2/3 = r^22 / r^27

To simplify the equation, we subtract exponents:
2/3 = r^(22-27)
2/3 = r^-5

Taking the reciprocal of both sides:
3/2 = r^5

Now, we can solve for r by taking the 5th root of both sides:
r = (3/2)^(1/5)

By calculating this value, we find that r ≈ 1.216.

Now that we know the common ratio (r), we can find the 43rd term (a43) using the formula:

a43 = a1 * r^(43-1)

However, we do not have the value of the first term (a1). Without the explicit value of a1, it is impossible to determine the exact value of the 43rd term in the geometric sequence. Therefore, we cannot provide the exact answer but can only explain the method to find it.