1. ## Sum to infinity

The sum to infinity of a geometric progression is 5 and the sum to infinity of another series formed by taking the first, fourth, seventh, tenth, ... terms (that is, U1+U4+U7+U10+...) is 4. Find the common ratio of the first series.

2. Hint

The ratio of the second series is the cube of the first one.

3. Originally Posted by FernandoRevilla
Hint

The ratio of the second series is the cube of the first one.
sorry but why is this so?

4. Originally Posted by Punch
sorry but why is this so?
Write the first series out: a + ar + ar^2 + ar^3 + ar^4 + ar^5 + ar^6 + ....

Now take the first, fourth, seventh, tenth etc. terms and draw the conclusion that was pointed out to you in post #2.