x Turn on thread page Beta
 You are Here: Home >< Maths

# Proofs - AS C1 & C2 watch

1. Could someone outline the proofs for:

Arithmetic Progressions (Series)
Geometric Progressions (Series)

Or alternatively link to sites which explain them. Thanks.
2. Arithmetic

(a) + (a + d) + (a + 2d) + ... + (a + (n-2)d) + (a + (n-1)d)
writen backward this is
(a + (n-1)d) + (a + (n-2)d) + ...+ (a + 2d)+ (a + d) + (a)

add these 2 together term by teram and you get
(2a + (n-1)d) + (2a + (n-1)d) + .... + (2a + (n-1)d)
n(2a + (n-1)d)
this is twice the total so the total is
(n/2)(2a + (n-1)d)
3. Geometric

S = a + ar + ar^2 + ... + ar^(n-1)

muliply this by r and you get

rS = ar + ar^2 + ar^2 + ... + ar^(n)

subtract the first from the second and you get
S - rS = a - ar^n = a(1 - r^n) (as all the middle terms are present in both series they cancel)

S(1-r) = a(1 - r^n)

so S = a(1 - r^n)/(1-r)
the quadratic expression proog is just completing the square on ax^2 + bx + c = 0

x^2 + b/ax + c/a = 0

(x + b/2a)^2 = -c/a + (b/2a)^2

(2ax + b)^2= b^2 - 4ac (just muliplying through by 4a^2)

2ax + b = +/-rt(b^2 - 4ac)

2ax = - b +/-rt(b^2 - 4ac)

x = [- b +/-rt(b^2 - 4ac)]/2a
5. Thanks

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 14, 2006
Today on TSR

### Did he block me?

What should I do?

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE