Question

1.What is the sum of the geometric sequence 8, –16, 32 … if there are 15 terms? (1 point)
2.What is the sum of the geometric sequence 4, 12, 36 … if there are 9 terms? (1 point)
3.What is the sum of a 6-term geometric sequence if the first term is 11, the last term is –11,264 and the common ratio is –4? (1 point)
4.What is the sum of an 8-term geometric sequence if the first term is 10 and the last term is
781,250? (1 point)

@Hero can you help me please with these geometric series equations! I don't understand them and need help!!!!!

Answer 1

Please allow someone else to help. I've been helping students all day and I have other stuff to do. It's jsut geometric series. So someone will help. Maybe @tkhunny

Answer 2

Good luck

Answer 3

Thanks anyways!!!! @Hero

Answer 4

@tkhunny please help! hero recommended you lol

Answer 5

I will give you medals on ALL of the answers you give me! @tkhunny

Answer 6

8, –16, 32 … if there are 15 terms? (1 point)

You must learn to add these. With only 15 terms, you could sit down with your calculator and get it. With 5000 terms, that will be harder. you MUST learn how to add these.

-16 = -2*8
32 = -2*(-16)

Do we believe that the common factor is -2?

Answer 7

Yes, the common ratio, r= -2

Answer 8

Perfect. We're almost done.

Here's your series: 8 + 8*(-2) + 8*(-2)^2 + ... + 8(-2)^14

Do you believe that?

Answer 9

What equation did you use? When I first attempted this, I used the equation I learned: a1-an(r^n)/1-r

Answer 10

I presume you mean (a1-a1(r^n))/(1-r)

Yes, that is fine. We were about to build that formula. If you already have it, feel free to use it.

a1 = 8
r = -2
n = 15

Go!

Answer 11

\[S_n=\frac{ a(1-r^n) }{ 1-r } ; r<1\]
\[S_n=\frac{ a(r^n-1) }{ r-1 } ; r>1\]
Where a denotes the first term of the sequence, n is the number of terms, and r is the common difference or ratio.

The formula above only apply for geometric series. Memorize it!

Answer 12

Yes! Okay so you have:
sn= 8-15(-2)/15-1