Question

The geometric mean between the first two terms in a geometric sequence is 32. if the third term is 4 find the first term

Answer 1

let the terms be a, ar, 4

4a = 32
a = 8 <---- done here

Bonus marks:

ar^2 = 4
8r^2 = 4
r^2 = 1/2
r = ± 1/√2

terms would be
8 , 8/√2, 8/√2^2
8 , 8/√2, 4

looks good,
a = 8

Answer 2

Forget the previous post, I didn't read it carefully
let the 3 terms be a, ar , ar^2

geometric mean of first two terms = √(a(ar)) = 32
a √r = 32 --> a = 32/√r

also ar^2 = 4 --> a = 4/r^2

32/√r = 4/r^2
32r^2 = 4√r
8r^2 = √r
64r^3 = r
r^2 = 1/64
r = ± 1/8
from a = 4/r^2
a = 4(1/64) = 256

Answer 3

Ty