Question

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

108, -18, 3, negative one divided by two, ...

Answer 1

Well it appears the pattern is division of -1/6 while the starting point is108. Because of that, I can write it in the form of
\[\sum_{n=1}^{\infty}ar ^{n}\]where a is the initial number, 108, and r is the pattern of -1/6. So writing this as a geo-series Ihave:
\[\sum_{n=1}^{\infty}108(\frac{ -1 }{ 6 })^{n}\]
Now a geometric series converges if the absolute value ofr is between 0 and 1. The absolutel value of r in this case is 1/6, so we definitely converge. In order to see where it converges to, we use this formula:
\[\frac{ a }{ 1-r }\]So can you plug in the appropriate numbers for a and r and find where your series converges to? :P

Answer 2

so r will be the ratio -1/6
so what is a ?

Answer 3

108, your initial number.

Answer 4

ok thanks

Answer 5

Mhm :3