Can someone please calculate this:

Question

48(-1/2)^6

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

Answer 1

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.

Answer 2

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!

Answer 3

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.

Answer 4

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

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

Answer 5

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