Finding Postion of the Nth Term
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Finding Postion of the Nth Term
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?
N = dN + (a-d)
Anyone know what's the formula for finding the position in a sequence of a term within that sequence?
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- Posts: 1245
- Joined: Fri Jul 06, 2007 9:31 pm
Finding Postion of the Nth Term
Thank you for your reply - I will try your suggestion.
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- Posts: 1245
- Joined: Fri Jul 06, 2007 9:31 pm
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
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
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- Posts: 1245
- Joined: Fri Jul 06, 2007 9:31 pm
So I was right... If a=3, d=2, and term being considered is 21...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
(N+(d-a))/d
(21+(2-3))/2
= 10
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