Question

What is the sum of the geometric sequence 1, 4, 16, ... if there are 8 terms?

Answer 1

1 + 4 + 16 + ... + 4^(n-1) + ... + 4^(7)

Are you SURE you can't add those up?

Personally, I'd do it this way: \(\dfrac{1 - 4^{8}}{1-4}\). You may have another formula based on a, r, and n.

Answer 2

I can add :) I just am mostly unsure of the equation to use. But YES! The equation I'm supposed to use involves a, r, and n!

Answer 3

Okay, then what is preventing you from using it?

a = 1
r = 4
n = 8

Go!

Answer 4

Funny story: I do online classes and I am usually very good at following formulas. Although for whatever reason the review equations that I applied to my previous homework made me get EVERYTHING wrong! So now I have no idea which kind of equations to use, on which kind of geometric series or sequences or arithmetic sequences or series

Answer 5

Sad, sad, how many of these online courses just don't seem to be doing the job they claim to be doing!

Arithmetic Sequence

Each successive term differs from its predecessor by a constant.

Example: 1, 2, 3, 4, 5, ... Each term is one (1) great than the previous.


Geometric Sequence

Each successive term differs from its predecessor by a ratio.

Example: 1, 2, 4, 8, 16, ... Each term is twice the previous.

Okay, what sort of Series have you?

Answer 6

I'm actually one the very end of my course and sudden;y everything that i'm learning is wrong :(
the one I just posted would be a geometric sequence, right?

Answer 7

yes it is a geometric sequence with r=4 meaning that every next number is multiplied by four: \[\sum_{n=1}^{8}4n\]so literally you're just adding it up
\(1+4+16+64+256+1,024+4,096+16,384=21,845\)