series and sequences question (1 Viewer)

[hornsbystudylad]

ignore the fact that geometric sequence is non-constant - help please!

 

[cossine]

View attachment 37141
ignore the fact that geometric sequence is non-constant - help please!

Give the question a go. How are the terms of geometric sequence defined?

 

[Lith_30]

Since there are two possible values for a and c, we might need to consider a quadratic equation. Lets work backwards a little to see what quadratic we need.

So this quadratic has roots of 1 and 9
We need to be on the lookout for something like this hopefully

now lets set up the equations
we'll let r be the common ratio between a,b,c



and for the arithmetic sequence we shall make the common difference be d



now what we have to do is to create an equation with only a and c (hopefully a quadratic), this can be done by finding two equations with just the variables a,b,c ie we need to find a way to remove r and d.

looking at equations and divide them to get

then we sub that new equation into to take out the r...

Now lets look at equations and , subtract both of them to get



now that we have our two equations, lets sub into remove the b



yo it is da quad equation , the rest should be pretty easy.