I don't know why I keep getting this question wrong. Can someone help please?
Identify the 16th term of a geometric sequence where a1 = 4 and a8 = -8,748
(A) -172,186,884
(B) -57,395,628
(C) 57,395,628
(D) 172,186,884

Question

I don't know why I keep getting this question wrong. Can someone help please?
Identify the 16th term of a geometric sequence where a1 = 4 and a8 = -8,748
(A) -172,186,884
(B) -57,395,628
(C) 57,395,628
(D) 172,186,884

anonymous · Answer

$$a_n = a_1*r ^{n-1}$$

anonymous · Answer

Find the ratio between each term, then use that equation, using n=16

jdoe0001 · Answer

$\large \begin{array}{llll}
term&value
\\hline\
a_1&4\
a_2&4r\
a_3&(4r)r\
a_4&(4rr)r\
a_5&(4rrr)r\
a_6&(4rrrr)r\
a_7&(4rrrrr)r\
a_8&(4rrrrrr)r=-8748
\end{array} $


     what does that give you for the commond ratio "r"?

anonymous · Answer

I'm sorry, i do not understand.

anonymous · Answer

I am not used to using "r"

jdoe0001 · Answer

hmm    do you know what a geometric sequence is?

anonymous · Answer

Yes, I do.

jdoe0001 · Answer

well... 
common ratio "r"
is just the multiplier

we dunno what the multiplier is, to get the next term
but we do know that, it's used each time, every time to get the "next term"

notice above

so.... notice the last term there, the 8th one
"r" was used 7 times to get there, that is, to get -8748

so.... solving for "r", that gives us?

jdoe0001 · Answer

hmm got a minus there for some reason... lemme fix that

jdoe0001 · Answer

once you get the "r"
the rest is peanuts
as larryboxaplenty  already pointed out 

$\bf a_{\color{brown}{  n}}=a_1{\color{blue}{  r}}^{{\color{brown}{  n}}-1}\qquad {\color{brown}{  n}}=16\qquad a_{\color{brown}{  16}}=a_1{\color{blue}{  r}}^{{\color{brown}{  16}}-1}
$

anonymous · Answer

I think he/she is confused on finding "r"

jdoe0001 · Answer

hmm pretty straightforward it seems though

anonymous · Answer

Yes. I am confused on finding "r" 
I am sorry.

jdoe0001 · Answer

hmm
ahemm one sec

jdoe0001 · Answer

$\large \begin{array}{llll}
term&value
\\hline\
a_1&4\to& 4\
a_2&4r\to &4r\
a_3&(4r)r\to &4r^2\
a_4&(4rr)r\to &4r^3\
a_5&(4rrr)r\to &4r^4\
a_6&(4rrrr)r\to &4r^5\
a_7&(4rrrrr)r\to &4r^6\
a_8&(4rrrrrr)r\to &4r^7=-8748
\end{array}$

     ok... see the equation?   what do you think is "r"?

anonymous · Answer

Lol, I got the answer! Thank you! Sorry, this stuff was just going right over my head. Thank you all for your help!

wolf1728 · Answer

Gee, I was all set to tell you:

r^7 = -8,748/4

r^7 = -2,187

r = 7th root of -2,187

wolf1728 · Answer

anyway, u r welcome