1. ## Text Book Error?

I'm back with another potential error in the textbook by Chandler/Bostock, Core Course for A Level. Last time it was my mistake, but this time I am more confused:

Page 594, Question 8

The sum of the first n terms of a series is given by Sn = n(3n-4). Show that the terms of the series are in arithmetic progression.

Can this be right?

2. ## Re: Text Book Error?

The test book is correct. You need to prove that the under lying sequence whose sum is given by $S_n$ is in A.P. Did you try considering $S_n - S_{n-1}$?
Spoiler:
Given
$S_n = \sum u_n = n(3n-4)$. Consider $S_n - S_{n-1} = u_n = n(3n-4) - (n-1)(3(n-1)-4) = 6n-5 = 6(n-1)+1$
Similarly we have
$S_{n-1} - S_{n-2} = u_{n-1} = (n-1)(3(n-1)-4) - (n-2)(3(n-2)-4) = 6n-11 = 6(n-2)+1$

So they are in A.P with $u_n = 6(n-1)+1$ where $a=1, d=6$

3. ## Re: Text Book Error?

Ok, I can see where I have got confused now. It's one of those horrible oversights that seems silly when you realise. Thanks.

4. ## Re: Text Book Error?

Actually, to be fair to the book, both cases that I have questioned have turned out to be careless errors from me. I think that is also a normal phenomenon