1. ## Tricky One Here!

Hey guys, (and girls), I'm new here and I was wondering if someone could get me started on this problem:

Find y so that (4y+1)+(y+4)+(10-y) form a geometric series.

So far, I know the following:

T1=4y+1
T2=y+4
T3=10-y

Tn=ar^(n-1)

EDIT: I also know that I need to find 2 anwsers for r.

2. Originally Posted by Gasser666
Hey guys, (and girls), I'm new here and I was wondering if someone could get me started on this problem:

Find y so that (4y+1)+(y+4)+(10-y) form a geometric series.

So far, I know the following:

T1=4y+1
T2=y+4
T3=10-y

Tn=ar^(n-1)

EDIT: I also know that I need to find 2 anwsers for r.
You would know that for a geometric series $\displaystyle r = \frac{T_{n+1}}{T_n}$. In other words, the ratio of a term to the previous term is r.

So you require $\displaystyle r = \frac{y+4}{4y+1} = \frac{10-y}{y+4}$.

$\displaystyle \frac{y+4}{4y+1} = \frac{10-y}{y+4} \Rightarrow (y + 4)^2 = (4y + 1)(10 - y)$.

Expand, simplify and r-arrange into quadratic = 0. Solve the quadratic for y. Sub the value of y into either $\displaystyle r = \frac{y+4}{4y+1}$ or $\displaystyle r = \frac{10-y}{y+4}$ to get r.

3. ## Thanks

Thanks alot, that seems alot easier now