Question

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

60, -10, five divided by three, negative five divided by eighteen, ...

Answer 1

@jdoe0001

Answer 2

\(\bf \textit{sum of an infinite geometric serie}=\Sigma_{i=0}^\infty\quad a_1\cdot r^i=\cfrac{a_1}{1-r}\)

so... .we know the 1st term term... is there.. just 60
to find "r" in a geometric sequence... just divide the "next term" by the "current term" and that will spit out the multiplier "r"

Answer 3

convergent... means it ends somewhere at some number
divergent... means.. it doesn't have a limit, it just keep on going

Answer 4

so.. get "r" and plug it in at \(\large \bf \cfrac{a_1}{1-r}\) if it gives a value, that's it's limit, it ends there, thus is convergent

Answer 5

r=-6?

Answer 6

well.. not quite. close

Answer 7

\(\bf \cfrac{-\cancel{ 10 }}{\cancel{ 60 }}=?\)

Answer 8

6

Answer 9

is it positive 6?

Answer 10

-1/6?

Answer 11

hehe... yes.. -1/6 so there :)... just plug that in

Answer 12

\(\bf \cfrac{60}{1-\left(-\frac{1}{6}\right)}\)

Answer 13

360/7

Answer 14

yeap.... so it ends somewhere.. thus is convergent

Answer 15

wheres the limit?

Answer 16

360/7 <--

Answer 17

hmm, that's not of my answer choices :/

Answer 18

hmm 51.43 I'd think is the decimal of that

Answer 19

yes, but it is still not of my answer choices.

Answer 20

hmmm what are the choices given? I don't see anything wrong there

Answer 21

Diverges

Converges; 11100

Converges; 72

Converges; 0

Answer 22

i think r was suppose to be positive, 1/6, so we get the limit 72. we are multiplying 1/6 everytime.

Answer 23

hmmm ....

Answer 24

so....... can't be.... is a negative 2nd and rth term... so is a negative "r"

Answer 25

2nd and 4th term I meant.... but.... hmmm nope.. looks to me ok with 360/7

Answer 26

maybe the negatives aren't meant to be there... or someone forgot to add the minus to the 1/6 when getting the choices done

Answer 27

i will ask my teacher about it.

Answer 28

it happens =)

Answer 29

everyone makes mistakes C;