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Finding Postion of the Nth Term
Posted: Thu Jan 07, 2010 3:38 pm
by ealingmum
The formula for finding the Nth term of a sequence is
N = dN + (a-d)
Anyone know what's the formula for finding the position in a sequence of a term within that sequence?
Posted: Thu Jan 07, 2010 4:08 pm
by SunlampVexesEel
I don't understand the question... do you have any sub- or super-scripts missing?
But I would guess... re-arrange
gives
(N+(d-a))/d
Finding Postion of the Nth Term
Posted: Thu Jan 07, 2010 4:22 pm
by ealingmum
Thank you for your reply - I will try your suggestion.
Posted: Thu Jan 07, 2010 4:32 pm
by Warks mum
For some reason, I feel the need to work out N:
N = dN + (a-d)
Take dN away from both sides:
N- dN = (a-d)
Which is the same as:
N(1-d) = (a-d)
Divide both sides by (1-d)
N = (a-d)/(1-d)
Posted: Thu Jan 07, 2010 9:10 pm
by ealingmum
No this doesn't work - how do they expect 11 year old to do this!
Posted: Thu Jan 07, 2010 10:20 pm
by SunlampVexesEel
I feel we don't have the whole question....
Posted: Thu Jan 07, 2010 11:30 pm
by heather
The formula N = dN + (a-d) isn’t really correct –
N on the left hand side is the value of the Nth term, and N on the right hand side is the term number, so two different letters are required. d is the common difference, and a is the value of the first term
For example, take the sequence 3, 5, 7, 9, 11, ………….
Then, if we let the value of the Nth term be y, we would have
y=dN +(a-d)
say we want to find the value of the 8th term in the sequence.
Then,
Y =2 x8 +(3-2)
=16 +1
=17
Now for the original question: the formula for finding the position in a sequence of a term within that sequence?
Say we’re told that 21 is a number in the above sequence, but we need to find the position of it in that sequence; we can re-arrange the same formula – we know the value of y (21) and we need to find N.
So,
21 = 2N +(3-2)
Subtract (3-2) from each side:
21 –(3-2) =2N
21-1 =2N
N=10 i.e the 10th term in the sequence is the number 21
Posted: Fri Jan 08, 2010 12:31 am
by SunlampVexesEel
heather wrote:...
For example, take the sequence 3, 5, 7, 9, 11, ………….
...
Say we’re told that 21 is a number in the above sequence, but we need to find the position of it in that sequence; we can re-arrange the same formula – we know the value of y (21) and we need to find N.
So,
21 = 2N +(3-2)
Subtract (3-2) from each side:
21 –(3-2) =2N
21-1 =2N
N=10 i.e the 10th term in the sequence is the number 21
So I was right... If a=3, d=2, and term being considered is 21...
(N+(d-a))/d
(21+(2-3))/2
= 10
Posted: Fri Jan 08, 2010 5:33 pm
by ealingmum
Thank you for this explaination.
Slump.. I could get your formula to work in simple sequences like the one here but not ones where the sequence started say at 37 - but then maybe that was my mistake