Question

Determine whether the sequence converges or diverges. If it converges, give the limit.

108, -54, 27, -27/2, ...

Answer 1

what do you multiply one number by to get the next?

Answer 2

-.5

Answer 3

ok good

Answer 4

so if r is between one and zero it is continuous?

Answer 5

so since \(|-5|<1\) the whole thing will go to zero
hold on a sec

Answer 6

are you asking if the sequence converges, or if the sum converges? you have no plus signs there, just commas

Answer 7

Determine whether the \(\color{red}{ sequence}\) converges or diverges
yes it does converge, the terms get smaller and smaller

Answer 8

i believe it's asking what the sum would be if the sequence does converge

Answer 9

by which i mean they go to zero
this is nothing "continuous" about this, they are discrete numbers
and as for \(r\) you are not being asked (as far as i can tell) to compute a sum, like \[\sum ar^n=\frac{a}{1-r}\]
just the limit of the sequence

Answer 10

ooh okay okay

Answer 11

if they really want you to add, they should say find \[\sum108\times (-\frac{1}{2})^r\]

Answer 12

these are my answer choices,
converges, 210
diverges
converges, 540
converges, 0

Answer 13

we already know now that it doesn't converge

Answer 14

but i don't know how to find the limit of a sequence? I'm lost

Answer 15

@satellite73

Answer 16

this is a geometric series. with r =(-1/2)
Note: it converges if |r|<1 and diverges if |r|>1.
since r= |-1/2| =1/2 <1 it converges, now to find to what number it converges to, use this formula