Question

Whats the missing term in the geometric sequence 2, __, 50?

Answer 1

`10`

Explanation:

In a geometric sequence you multiply by some number `r` to get to the next term. So if we call our missing term `x` we know this:
`2*r = x`
`x * r = 50`

substitute...
`2*r *r = 50`

You could also think of each step in the sequence as multiplying by another `r`, so basically your first term times `r` and times `r` again gives you 50. or `2r^2 = 50`

Either way will get you there.
solve for r...
`2r^2 = 50`
`r^2 = 25`
`r= 5`
Not done just yet...
plug in `r` into one of the above equations...
`2*r = x`
`2*5 = x`
`10 = x`