Question

What is a possible value for the missing term of the geometric sequence?

50, ___, 450, ...

Answer 1

\(\Huge\color{blue}{ \sf 50 \times X=450 \div X }\)
where x is the common ratio

then, what each of the sides (in my original equation) is equal to, is the missing term.
or so called, "geometric mean"

Answer 2

you can make a common difference of 3

Answer 3

oops....common ratio of 3

Answer 4

How did you get the common ratio?
450/50 = 9

Answer 5

a,b,c are in G.P.
THEN\[\frac{ b }{ a }=\frac{ c }{b },or~b ^{2}=ac\]

Answer 6

\[\{ if x is the \middle term ,then x ^{2}=50*450}\]
\[x=\pm \sqrt{50*450}=\pm 50*3=\pm 150\]
if x=150 ,c.r.=150/50=3
terms are 50,150,450,1350,....
if x=-150,c.r.=-150/50=-3
terms are 50,-150,450,-1350,...
terms are alternately positive and negative.