Question

Find the three geometric means between 2 and 162.

Answer 1

do you know what a geometric sequence is?

Answer 2

Nope.

Answer 3

then how do you usually work this sort of problem?

Answer 4

This is my first one. ><

Answer 5

if there is a certain number of geometric means between 2 values ... say we want 2 geometric means between k and j

kr^0 = k

kr^1 = 1 geo mean

kr^2 = 2 geo mean

kr^3 = j

if we know r, we can assess the geo means

Answer 6

Uhh... I'm sorry, I'm dumb, what do you mean?

Answer 7

the list of numbers generated from k to j ... forms a geometric sequence.

so 2r^4 = 162, we solve for r, to determine the 3 values that make our solution

2r^0 = 2
2r^1
2r^2
2r^3
2r^4 = 162

Answer 8

Oh, so it's finding what 3 numbers would go into the sequence between 2 and 162??

2, 6, 18, 54, 162 sound right? I multipled by 3...

Answer 9

let G1,G2,G3 be three G.M's between 2 and 162
so 2,G1,G2,G3,162 form a geometric sequence.
no. of terms=5
first term=2
t5=162
let r be c.r.
\[tn=ar ^{n-1}\]
where a is first term
find r
then G1=ar=2r
G2=G1*r
G3=G2* r