Question

insert 4 terms in geometric sequence between 3/8 and 128/81

Answer 1

insert?

Answer 2

lol, must be a homework question with 4 textboxes.

Answer 3

\[\frac{3}{8},\frac{128}{81},-,-,-,-\]
or

\[\frac{3}{8},-,-,-,-,\frac{128}{81}\]

???

Answer 4

the second one sorry it was meant to say between 3/8 and 128/81

Answer 5

do you recall the general setup for a geometric seq? that might prove useful

Answer 6

it can be done with means, but i find that technique a little obtuse :)

Answer 7

given:\[g_1=\frac38~:~g_6=\frac{128}{81}\]
and the general formula for a geo seq:\[g_n=g_1~r^{n-1}\]
we can solve this for "r"\[\frac{g_n}{g_1}=r^{n-1}\]\[\left(\frac{g_n}{g_1}\right)^{\frac{1}{n-1}}=r\]
use g6 to determine the r value to use in finding g2 g3 g4 and g5