C2 maths q

A geometric series has first term a and common ratio r.

The second term of the series is 4 and the sum to infinity of the series is 25.

(a) Show that 25r

2 – 25r + 4 = 0.

(4)

(b) Find the two possible values of r.

(2)

(c) Find the corresponding two possible values of a.

(2)

(d) Show that the sum, Sn, of the first n terms of the series is given by

Sn = 25(1 – r

n

).

(1)

Given that r takes the larger of its two possible values,

(e) find the smallest value of n for which Sn exceeds 24.

I have no clue on which formula to use to prove/show the thing they want us to show in (a.) If i got a i think i could do b by just factorising. and then im also struggling with (e.) as i have no clue once again how to show this? would i sub in the largest r value and use that to find n or??

The two formulae they want you to use in part a are... almost given away by the question.

Nth term and sum to infinity.

okay thank you, sorry but i struggle with maths so dont understand it as easily

If a geometric series has first term a and common ratio r, what is the second number in the sequence in terms of a and r?

If a and r are described as above, what is the sum to infinity of that sequence?

If a geometric series has first term a and common ratio r, what is the second number in the sequence in terms of a and r?

If a and r are described as above, what is the sum to infinity of that sequence?

ok so ive done b and c and now im not sure what values to use in d?!

D wants it in terms of a and r.

Hint: see the link between sum to infinity and sum to n terms in this question.

im sorry but im not really seeing what i need to do...

There is a hint in the question - 25 is part of the sum to n terms... where do you recognise this from?

im not sure the first bit??