The Nth Term....My Nemesis (need help)

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Report 17 years ago
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Hey all, i need your help with a GCSE work based problem. Im home educated so i cant really ask a teacher, and im about 3 weeks from going back to my Revision center.

My problem is with an Nth Term question in my CGP Revision guide (i realise they are known for being iffy, but revision books are extremely expensive), it goes as follows;

"The formula for finding the Nth term in a number sequence with a changing difference is: a + (n - 1)d + 1/2(n - 1)(n - 2)C
where 'a' = First term
'd' = First difference
'C' = change in difference
Find the nth term for this sequence: ' 2 , 5 , 9 , 14 "

Now i get all that perfectly fine, its the example Question and answer that stumps me;

"[putting the sequence into the formula] this gives;

2 + (n-1)3 +1/2(n - 1)(n - 2) x 1"

now, you would have though that seeing as this is on page 8, and all the algebra stuff is right at the end of book (ive done that btw, Nth terms are a continuing problem for me) they would have given an in-depth example of how to solve this, but they dont. It skips right onto;

"2 + 3n - 3 + 1/2n^2 - 1.5n + 1"

.............WTF!? i can get the '2 + 3m - 3' part, and even some of the '1/2n^2 - 1.5n + 1' but its the extra 'n' on the end of the '1.5n + 1' that i dont understand. Where does it come from??

Please help, and explain in basic, yet detailed instructions....im not too quick when it comes to maths (as you may be able to tell)

thank in advance

- Guiberu
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2 + (n-1)3 +1/2(n - 1)(n - 2) x 1"

becomes

"2 + 3n - 3 + 1/2n^2 - 1.5n + 1"

like this

2 => 2 (duh!)
(n-1)3 => 3n - 3
+1/2(n - 1)(n - 2) x 1 => 1/2(n^2 -2n -n +2) x1 => 1/2n^2 -n -1/2n + 1 => 1/2n^2 -1.5n + 1

Okay?
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