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1. (show the full calculations)
(a). The n^th term of a sequence is n(n+1)
(i) Write the two missing terms in the spaces.
2, 6, ___, 20, ___
(ii) Write down an expression in terms of n for the 〖(n+1)〗^th term.
___________.
(iii) The difference between the n^th term and the 〖(n+1)〗^th term is pn+q.
Find the values of p and q.
(iv) Find the positions of the two consecutive terms which have a difference of 140
__________ and __________.



Answer :

Hippalectryon
i)
2=1*2
6=2*3
the first missing term is 3*4=12
20=4*5
the second missing term is 5*6=30

ii) Let a(n) be the nth term, then a(n+1)=(n+1)(n+2)=n^2+3n+2

iii) a(n+1)-a(n)=(n+1)(n+2)-n(n+1)=(n+1)(n+2-n)=2n+2 hence p=2,q=1

iv) Given question iii), we need to solve 2n+2=140 hence n=69
The two terms are 69 and 70 : (70*71)-(69*70)=140

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