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

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

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, ...

anonymous · Answer

@jdoe0001

jdoe0001 · Answer

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

jdoe0001 · Answer

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

jdoe0001 · Answer

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

anonymous · Answer

r=-6?

jdoe0001 · Answer

well.. not quite. close

jdoe0001 · Answer

$\bf \cfrac{-\cancel{ 10 }}{\cancel{ 60 }}=?$

anonymous · Answer

6

anonymous · Answer

is it positive 6?

anonymous · Answer

-1/6?

jdoe0001 · Answer

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

jdoe0001 · Answer

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

anonymous · Answer

360/7

jdoe0001 · Answer

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

anonymous · Answer

wheres the limit?

jdoe0001 · Answer

360/7   <--

anonymous · Answer

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

jdoe0001 · Answer

hmm 51.43 I'd think is the decimal of that

anonymous · Answer

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

jdoe0001 · Answer

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

anonymous · Answer

Diverges

 Converges; 11100

 Converges; 72

 Converges; 0

anonymous · Answer

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

jdoe0001 · Answer

hmmm     ....

jdoe0001 · Answer

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

jdoe0001 · Answer

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

jdoe0001 · Answer

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

anonymous · Answer

i will ask my teacher about it.

jdoe0001 · Answer

it happens =)

anonymous · Answer

everyone makes mistakes C;