Question

Find the sixth term of a geometric sequence with t5 = 24 and t8 = 3.

Answer 1

t5 = a*r^4 = 24
t8 = a.r^7 = 3

So now what do you do?

Answer 2

I just saw the exact same post and to me that didn't make any sense

Answer 3

@♂

Answer 4

We are dividing one by the other...
\[R ^{3}\] = 1/8
r = 1/2
t6 = a.r^5 = t5*r = 24 * 1/2 = 12

Answer 5

R^3=1/8

Answer 6

the first part makes sense and the second but how did you get r^3 = 1/8 That's the part I don't get. I know you said divide, and 24/3 equals 8. but why 1/8

Answer 7

the way I'd do it, is:
\(24=t_5\\24*r=t_6\\
24*r^2=t_7\\
24*r^3=3=t_8\\24*r^3=8\implies r^3=\dfrac{1}{8}\\
\)
solve for r

Answer 8

r=1/2

Answer 9

@♂ thanks! that makes more sense now

Answer 10

hmm the geometric sequence's Nth term is
\[a_n=ar^{n-1}\] where a is the first term and r is the common ratio
so our goal here is to find those two
given the info

Answer 11

\[t_8=tr^{7}=3 \\ t_5=tr^4=25\]

Answer 12

from those two equations we can find what t the first term
and r the common ratio are

Answer 13

then we can find the sixth term
or any other term we desire to find

Answer 14

tr^4=24 not 25 correction!
and 1/2 is correct as suggested by the fellows above :)

Answer 15

well didn't see @iYuko work
decent work as well
grant him/her a medal too :)