Question

Whats the missing term in the geometric sequence 1, __, 49?

Answer 1

`2^("nd") " term " ->7`

`color(blue)("Have a look at the way the sequence is built!")`

Explanation:

As I understand it, a Geometric sequence is of structure:

`ar^0, ar^1, ar^2, ar^3......` where r is the Geometric Ratio

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Note that "r^0 = 1color(white)(...)" so "ar^0 = a`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In your case the first term `-> ar^0 =1` so `a=1`

Given that the third term `-> ar^2=49`
as `a=1 " then "1 xx r^2 =49`

So `sqrt(r^2)=r = sqrt(49) = 7`

The missing term `-> ar^1 = 1 xx 7^1`

`7^1 = 7 color(white)(...)`so the missing term is 7