Honours Maths question... (Sequences and series)

Mutant_Fruit

the actual 1994 paper (not any of the samples), paper 1, question 4 b(i).

The sum of the first n terms of a series is given by n(n-1). Write Un in terms of n.

I presumed that Sn - S(n-1) = Un. Doing that i got an answer of (2n-1).

BUT, if do this: S(n+1) - Sn i get an answer of (2n).

Shouldn't both of these give the same answer? And which is the corrent answer, and why is one wrong?


EDIT: Either way (whether i use (2n) or (2n-1), when i work out the answer for b(ii) i get 16 as the answer. And i should get 0.

Mutant_Fruit

Its ok, i figured it.

For part (i), when i did the Sn - S(n-1), that was the right way. That gave me Un.

When i did it the other way, i got U(n+1).

As for part (ii), i give up. I assume the papers must be wrong again. I keep getting 16.

jackwalli

Mutant_Fruit - I've done part (ii) out and i got 16 too, here are my workings:

Un = 2n – 2
U(n+1) = 2(n+1) – 2 = 2n
U(n+2) = 2(n+2) – 2 = 2n + 2
U(n+3) = 2(n+3) – 2 = 2n + 4

[U(n+3)]^2 - [U(n+1)]^2 - [U(n+2)^2 – (Un)^2]
= 4n^2 + 16 + 16n – 4n^2 – 4n^2 – 8n – 4 + 4n^2 – 8n + 4
= 16n + 16 – 16m
= 16

Educational Company seem to love teasing us with the wrong answers in the back of the papers.

PrecariousNuts

Yes the answer is 16 those smegheads got it wrong again.