Can someone please calculate this:

48(-1/2)^6

The answer is 3/2, but I get 3/4. What am I dong wrong?

You didn't do anything wrong.

Either there is a typo in the question or the answer.

If the power had been ^5, then the answer should have been -3/2. So there's something wrong somewhere.

Thank you for responding. Hmm... IDK. . .I'll have to ask if that's a typo on the other end. Hey do you mind seeing if this is correct, and helping with the second part?

Consider the geometric sequence that begins -3072 and common ratio –1/2.

Find the 13th and 20th terms of this sequence.
a₁₃ = -3072(-1/2)¹² = -3/4
a₂₀ = -3072(-1/2)¹⁹ = -0.005859375
Is this right?

b. Find the sum of the first nine terms.
I'm not sure what to do here. . .

Thank you again for your help!

a13 is correct.

I get for a20 -3072(-1/2)^19=3/512 (i.e. positive, not negative)

The sum of the first n terms of a geometric sequence of initial value a, and common ratio r is
=a(1+r+r^2....+r^(n-1) )
=a(r^n-1)/(r-1)

So substitute the values to get your answer.

So, this is how far I got. . .I getting weird numbers. . .

-3072(1 - (-1/2)⁹)
------------------- =
1 - (-1/2)

Don't know if you tried, it gives -2052.

If you calculate the nine terms
minus plus
3072 1536
768 384
192 96
48 24
12
----------
4092 2040

-4092+2040=-2052

To solve the expression 48(-1/2)^6, we need to follow the order of operations which is typically represented by the acronym PEMDAS or BODMAS. It stands for Parentheses (or Brackets), Exponents (or Order or Indices), Multiplication (or Division), and Addition (or Subtraction). Let's break down the steps:

1. Parentheses (or Brackets): There are no parentheses involved in this expression, so we can move to the next step.

2. Exponents (or Order or Indices): In this case, we have an exponent. The exponent of 6 applies to (-1/2). So, (-1/2)^6 means we need to multiply -1/2 by itself six times.

(-1/2)^6 = (-1/2) * (-1/2) * (-1/2) * (-1/2) * (-1/2) * (-1/2)

3. Multiplication: Now, we perform the multiplication from left to right using the multiplication operator (*).

(-1/2) * (-1/2) = (1/2) * (1/2) = 1/4
(1/4) * (-1/2) = -1/8
(-1/8) * (-1/2) = 1/16
(1/16) * (-1/2) = -1/32
(-1/32) * (-1/2) = 1/64
(1/64) * (-1/2) = -1/128

4. Multiplication: Finally, we multiply the result by 48.

48 * (-1/128)

By multiplying across, we get -48/128, which can be simplified to -3/8.

Therefore, the result of the expression 48(-1/2)^6 is -3/8, not 3/2 as you mentioned.

It seems like there might have been a mistake in your calculations. Double-check the multiplication steps to ensure accuracy.