Question

In a geometric series, t1=12 and s3=372.what is the greatest possible value for t5?

Answer 1

so, we know
a = 12 and
372 = 12(r^3 - 1)/(r-1) ,divide by 12, then multiply both sides by r-1
31r - 31 = r^n - 1
r^3 - 31r+ 30 = 0

by inspection I saw that r=1 works
so r-1 is a factor
by synthetic division
I got (r-1)(r-5)(r+6) = 0
r = 1, 5, -6

if r=1 , t5 = ar^4 = 12(1^4) = 12 , all terms would stay the same
if r=5, t5= 12(5)^4 = 7500

if r = -6 , t5 = 12(-6)^4 = <b>+ 15552 -- the greatest</b>

btw, if r = -6
terms are : 12 , -72 , 432 , -2592 ...
and 12 - 72 + 432 = 372

Answer 2

Thank you so much could you please answer the other question my friend jim put up

Answer 3

Your friend jim ?
but you posted as jim !

Now do you see why we don't want you to switch names?
You get yourself confused and you don't even know who you are !

Btw, check for that post under bob/jim