G.P.

• Feb 15th 2010, 03:49 AM
Sunyata
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...
• Feb 15th 2010, 04:07 AM
Prove It
Quote:

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 $y$.
• Feb 15th 2010, 04:10 AM
Sunyata
What does it mean by convergent?
• Feb 15th 2010, 04:16 AM
Prove It
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 $\infty$.