Why delta Sn = Sn - S(n-1)?

[Indranil]

I am giving an equation from Physics.'delta Sn = Sn - S(n-1)' (a screenshot)
Now my question is why the distance to the first part is 'S(n-1)' (why (n-1) used here) If the total distance is 'Sn'?
As I know, If the total distance or final distance would be x2 and initial distance would be x1, the difference between the two distance is delta x = x2 - x1.

 

[Dr.Peterson]

I am giving an equation from Physics.'delta Sn = Sn - S(n-1)' (a screenshot)
Now my question is why the distance to the first part is 'S(n-1)' (why (n-1) used here) If the total distance is 'Sn'?
As I know, If the total distance or final distance would be x2 and initial distance would be x1, the difference between the two distance is delta x = x2 - x1.

Do you understand that S_n is a sequence of positions at successive times (one second apart), so that the term before S_n is S_n-1 (that is, the term before the nth term is the (n-1)st)?

At one time, the total distance moved is S_n-1, and a second later it has moved to S_n, so the distance traveled over that period of time is S_n - S_n-1.

For example, if n is 2, then n-1 is 1, so you are doing exactly what your delta formula says: S₂ - S₁.

 

[Indranil]

Do you understand that S_n is a sequence of positions at successive times (one second apart), so that the term before S_n is S_n-1 (that is, the term before the nth term is the (n-1)st)?

At one time, the total distance moved is S_n-1, and a second later it has moved to S_n, so the distance traveled over that period of time is S_n - S_n-1.

For example, if n is 2, then n-1 is 1, so you are doing exactly what your delta formula says: S₂ - S₁.

From the explanation above, could you simplify 1. 'nth' term? and
2. the 'n-1' form and why it is used here? (as I know 'n = time' here)

 

[Dr.Peterson]

From the explanation above, could you simplify 1. 'nth' term? and
2. the 'n-1' form and why it is used here? (as I know 'n = time' here)

Please don't just ask to "simplify". Tell us what you find complicated about it!

Are you saying you have never heard of "the nth term"? Do you not know what a sequence is? Or is it the English that is confusing you?

A sequence consists of a list of terms, each corresponding to a number called the index. Term number 1 (index 1) is the first (1st) term. Term number 2 is the second (2nd) term. Term number 3 is the third (3rd) term. Term number 4 is the fourth (4th) term. Term number n (index n) is the nth term.

For example, in the sequence 1, 1, 2, 3, 5, 8, 13, the 6th term is 8; if n=6, we say the nth term is 8.

If we replace n with n+1, we are talking about the next term; if we replace n with n-1, we are talking about the previous term.

 

[Deleted member 4993]

From the explanation above, could you simplify 1. 'nth' term? and
2. the 'n-1' form and why it is used here? (as I know 'n = time' here)

As I had suggested before - you need a face-2-face teacher. You could also look into enrolling in a Community College and register for developmental Mathematics.

 

[Indranil]

Please don't just ask to "simplify". Tell us what you find complicated about it!

Are you saying you have never heard of "the nth term"? Do you not know what a sequence is? Or is it the English that is confusing you?

A sequence consists of a list of terms, each corresponding to a number called the index. Term number 1 (index 1) is the first (1st) term. Term number 2 is the second (2nd) term. Term number 3 is the third (3rd) term. Term number 4 is the fourth (4th) term. Term number n (index n) is the nth term.

For example, in the sequence 1, 1, 2, 3, 5, 8, 13, the 6th term is 8; if n=6, we say the nth term is 8.

If we replace n with n+1, we are talking about the next term; if we replace n with n-1, we are talking about the previous term.

I don't understand

1. 'Term number 1 (index 1) is the first (1st) term. Term number 2 is the second (2nd) term. Term number 3 is the third (3rd) term. Term number 4 is the fourth (4th) term. Term number n (index n) is the nth term.' what is 'index' number here?

2. 'in the sequence 1, 1, 2, 3, 5, 8, 13, the 6th term is 8; if n=6, we say the nth term is 8.' Why did you put the numbers in 1, 1, 2, 3, 5.... not 1,2,3,4,5.....?

3. 'If we replace n with n+1, we are talking about the next term; if we replace n with n-1, we are talking about the previous term.' If n=6, (n+1) = 7 but there is no 7 in the sequence above.

 

[Dr.Peterson]

!

I don't understand

1. 'Term number 1 (index 1) is the first (1st) term. Term number 2 is the second (2nd) term. Term number 3 is the third (3rd) term. Term number 4 is the fourth (4th) term. Term number n (index n) is the nth term.' what is 'index' number here?

2. 'in the sequence 1, 1, 2, 3, 5, 8, 13, the 6th term is 8; if n=6, we say the nth term is 8.' Why did you put the numbers in 1, 1, 2, 3, 5.... not 1,2,3,4,5.....?

3. 'If we replace n with n+1, we are talking about the next term; if we replace n with n-1, we are talking about the previous term.' If n=6, (n+1) = 7 but there is no 7 in the sequence above.

1. The index is the number of the element. Did I not make that clear?

2. The terms of my example sequence are 1, 1, 2, 3, 5, 8. The value of the term is not the same as the index.

3. The index is not the term! There are 7 terms in the sequence I listed (though I could have continued it); the 7th is 13. So here, n is 7 (the index of the 7th term), but the term itself, a₇, is 13.

I have to agree with others who have advised you to take a course, rather than trying to learn all of mathematics at once by asking questions with no context. This is not working for you. You must go back to the beginning and learn in an orderly way. At the very least, go through a book with a chapter on sequences, which will tell you all these things at the start. Or find an online course. Here are some sites that tell you these things:

https://www.mathsisfun.com/algebra/sequences-series.html

http://www.sosmath.com/calculus/sequence/intro/intro.html

 

[Indranil]

1. The index is the number of the element. Did I not make that clear?

2. The terms of my example sequence are 1, 1, 2, 3, 5, 8. The value of the term is not the same as the index.

3. The index is not the term! There are 7 terms in the sequence I listed (though I could have continued it); the 7th is 13. So here, n is 7 (the index of the 7th term), but the term itself, a₇, is 13.

I have to agree with others who have advised you to take a course, rather than trying to learn all of mathematics at once by asking questions with no context. This is not working for you. You must go back to the beginning and learn in an orderly way. At the very least, go through a book with a chapter on sequences, which will tell you all these things at the start. Or find an online course. Here are some sites that tell you these things:

https://www.mathsisfun.com/algebra/sequences-series.html

http://www.sosmath.com/calculus/sequence/intro/intro.html

Thanks for providing sites.