Question

Help? :P
Write the sum using summation notation, assuming the suggested pattern continues.

5 - 15 + 45 - 135 + ...

Answer 1

@whpalmer4

Answer 2

Can you decipher the pattern?

Answer 3

Not really, I eventually just had to plug each one into the answer choices..

Answer 4

Pretend all of the terms are either positive or negative? Could you write the pattern in summation notation then?

Answer 5

*3

Answer 6

a_n=a_(n-1)*3?

Answer 7

So the pattern is multiplying by 3, but also multiplying every other term by -1, wouldn't you agree?

Answer 8

Can you think of a sequence which just goes 1, -1, 1, -1, 1, -1...

is that arithmetic, geometric, ???

Answer 9

Uhmm... Arithmetic?

Answer 10

Isn't each term simply the previous term multiplied by -1? Isn't that a geometric series with a common ratio of -1?

Answer 11

An arithmetic one would have a common number added or subtracted to give the next term, but that doesn't work here.

Answer 12

Oh, got it. :p I was pretty sure I had that wrong.

Answer 13

So \((-1)^n = 1, -1, 1, -1, 1, -1, 1, -1...\) as \(n\) goes from \(0\) to whatever...

We could construct the string of numbers by using the geometric sequence
\[a_n = a_0r^{n-1}\]and multiplying it by \((-1)^{n-1}\) or
\[a_n = a_0r^{n-1}(-1)^{n-1} = a_0(-r)^{n-1}\]

Answer 14

Sooo... a_n=a_(n-1)*3^n?