Question

insert three geometric means between 16 & 625

Answer 1

ar^n-1=625
16r^5-1=625
r^4=625/16
r=±5/2

hence gm are ±40,±100,±250

Answer 2

Answer:hree geometric mean are 40,100,250

Step-by-step explanation:

let a, b, c are geometric mean between 16 and 625. so 16, x, y, z, 625 are in

G.P.

we know that nth teerm of G.P. is $ar^{n-1}$

so 5th term = 625

$16r^{5-1}=625\\\\r^{4}=\frac{625}{16}\\\\r=\frac{5}{2}$

x=ar =16*5/2

= 40

y=ar²

=16*25/4

=100

z=ar³

= 16*125/8

=250

so three geometric mean are 40,100,250