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November 5th, 2014, 07:59 AM  #1 
Newbie Joined: Mar 2012 Posts: 4 Thanks: 0  Algebraic Sequence. CIE past paper. Can't Solve :'(
How can question (iii) be solved (a) The nth term of a sequence is n(n+1). (i) Write the two missing terms in the spaces. 2, 6, , 20, [2] (ii) Write down an expression in terms of n for the (n + 1)th term. Answer(a)(ii) [1] (iii) The difference between the nth term and the (n + 1)th term is pn + q. Find the values of p and q. 
November 5th, 2014, 08:37 AM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,781 Thanks: 1432  Quote:
(ii) $\displaystyle a_n = n(n+1)$ ... to find $\displaystyle a_{n+1}$, substitute $\displaystyle (n+1)$ in for $\displaystyle n$ in the nth term (iii) once you determine the (n+1)st term, do the subtraction  
November 5th, 2014, 06:53 PM  #3 
Newbie Joined: Mar 2012 Posts: 4 Thanks: 0 
I was able to solve first and second question without any trouble. I was also able to determine the (n+1)th term. But in 3, I was not able to form the simultaneous equation! 
November 5th, 2014, 09:38 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,981 Thanks: 1853 
{iii) As (n + 1)((n + 1) + 1)  n(n + 1) = 2(n + 1) = 2n + 2, p = q = 2.


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