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November 5th, 2014, 06:59 AM   #1
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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.
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November 5th, 2014, 07:37 AM   #2
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Originally Posted by Kumail View Post
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.
(i) 1(1+1) = 2, 2(2+1) = 6, 3(3+1) = ? , 4(4+1) = 20, ...

(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
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November 5th, 2014, 05:53 PM   #3
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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!
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November 5th, 2014, 08:38 PM   #4
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{iii) As (n + 1)((n + 1) + 1) - n(n + 1) = 2(n + 1) = 2n + 2, p = q = 2.
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