Finding Postion of the Nth Term

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ealingmum
Posts: 156
Joined: Sat Jan 19, 2008 5:27 pm

Finding Postion of the Nth Term

Post 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?
SunlampVexesEel
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Post 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
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ealingmum
Posts: 156
Joined: Sat Jan 19, 2008 5:27 pm

Finding Postion of the Nth Term

Post by ealingmum »

Thank you for your reply - I will try your suggestion.
Warks mum
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Post 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)
ealingmum
Posts: 156
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Post by ealingmum »

No this doesn't work - how do they expect 11 year old to do this!
SunlampVexesEel
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Post by SunlampVexesEel »

I feel we don't have the whole question....
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heather
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Post 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
SunlampVexesEel
Posts: 1245
Joined: Fri Jul 06, 2007 9:31 pm

Post 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
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ealingmum
Posts: 156
Joined: Sat Jan 19, 2008 5:27 pm

Post 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
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