a geometric progression with 28 as its first term has the sum to infinity of 70 . find its common ratio .

a geometric progression with 28 as its first term has the sum to infinity of 70 .

find its common ratio

$$\text{sum: } \begin{array}{rlccl} s &=& 28 & + & 28r+ 28r^2 + 28r^3+28r^4+28r^5 +\dots+ \\ r*s &=& && 28r +28r^2+28r^3+28r^4+28r^5+\dots+ \\ \hline s-r*s &=& 28 &\\ &&&\\ \hline &&&\\ \end{array}$$

$$r*s = s - 28 \\ \\ r = \dfrac{s - 28}{s} \quad | \quad s = 70\\\\ r = \dfrac{70 - 28}{70} \\\\ r = \frac{42}{70} \\\\ r = \frac{21}{35} \\\\ r = \frac{3}{5} \\\\ r = 0.6$$

We have

28 / (1 - r)  = 70    rearrange

28/70  = 1 - r

r = 1 - 28/70  = 14/35

Oops.....i made a slight error here....I forgot to subtract the 28/70 from the 1...the correct answer is ..

1 - 28/70  = 42/70 = 21/35 = 3/5  .....now, it matches heureka's solution!!!!

Thanks for calling my attention to that, heureka...!!!  DOH !!!!

thank you very much both of you

Hi CPhill,

ditto!