# Math Help - G.P.

1. ## G.P.

Show that there are 3 geometrical progression in which the second term is - 4/3 and the sum of the first three terms is 28/9. SHow that one of these series is convergent and, in this case, find the limit of its sum.

How on EARTH do i do this question???

x - 4/3 + y = 28/9...

2. Originally Posted by Sunyata
Show that there are 3 geometrical progression in which the second term is - 4/3 and the sum of the first three terms is 28/9. SHow that one of these series is convergent and, in this case, find the limit of its sum.

How on EARTH do i do this question???

x - 4/3 + y = 28/9...
Since this is a geometric progression, you know that $t_{n + 1} = rt_n$.

Therefore $r = \frac{t_{n + 1}}{t_n}$.

So here $r = \frac{-\frac{4}{3}}{x}$ and $r = \frac{y}{-\frac{4}{3}}$.

Therefore $\frac{-\frac{4}{3}}{x} = \frac{y}{-\frac{4}{3}}$

$y = \frac{-\frac{4}{3}\left(-\frac{4}{3}\right)}{x}$

$y = \frac{\frac{16}{9}}{x}$

$y = \frac{16}{9x}$.

Therefore, the sum of the first three terms is

$x - \frac{4}{3} + \frac{16}{9x} = \frac{28}{9}$.

Solve for $x$ and then you can find $y$.

3. What does it mean by convergent?

4. It means that if you had an infinite number of terms, if you were to add them up, you would find that the sum tends to a number, rather than tending to $\infty$.