Question

a11=72 and a13=1/2 use the geometric mean to find the value of a12???

Answer 1

do you know what a geometric mean is?

Answer 2

the geometric mean of \(a\) and \(b\) is
\[\sqrt{ab}\]

Answer 3

I thought it was like the average # used during a pattern but idk not sure

Answer 4

it is what i wrote above

Answer 5

Ok I see it

Answer 6

multiply the numbers, then take the square root

Answer 7

a11,a12,a13
same as
ar,ar2,ar3
and here a=72,ar2=12 so
ar2a=r2=1272=1144

if r2=1144 then r=112

Answer 8

no

Answer 9

if you are using the geometric mean, then \[72\times \frac{1}{2}=36\] and
\[\sqrt{36}=6\]

Answer 10

or
\[ar=72, ar^2,ar^3=\frac{1}{2}\implies r^2=\frac{ar^3}{ar}=\frac{1}{2\times 72}=\frac{1}{144}\] this tells you \(r=\frac{1}{12}\) and so
\[72, 6, \frac{1}{2}\] is the sequence

Answer 11

Idk I got 16

Answer 12

Ill figure it out

Answer 13

\[\large \sqrt{ab}=\sqrt{72\times \frac{1}{2}}=\sqrt{36}=6\]is the computation