Maths help

[Luke]

I'm back again -.-

Completely forgot everything over the past 2 weeks, so.. could anyone help with this?
Cheers

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The second and fifth terms of a geometric series are 9 and 1.125 respectively.

For this series find
(a) - the value of the common ratio,
(b) - the first term,
(c) - the sum to infinity

[LoveToStack]

a) Ok so remember that the common ratio, r, is the thing which you are multiplying each new term by. So the first term is a, the second term is ar, then ar^2 and so on and so on.

I liked to imagine it as a line: a + ar + ar^2 + ar^3 + ...
So for your question you know the 2nd and 5th terms, which are the equivalent of 'ar' and 'ar^4'. Now if you divided ar^4 by ar, you would get r^3. Knowing that should let you find 'r'.

b) Once you know 'r', getting the first term 'a' is a piece of cake. Since you've got the values for the 2nd term (ar^2) and the 5th term (ar^4), all you need to do is setup an equation using either value and solve for a.

c) The sum of a geometric series is a/(1-r). You might be asked to derive the formula for the sum of an arithmetic series but I doubt you'll ever be asked to derive the sum to infinity of a geometric series since it involves limits.

[Luke]

Many Thanks