Derive the nth term of a sequence

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To derive the nth term of a sequence from the sum to the nth term, one can use the relationship between consecutive sums. For example, if Sum4 equals a1 + a2 + a3 + a4 and Sum3 equals a1 + a2 + a3, then a4 can be expressed as a4 = Sum4 - Sum3. This method allows for the calculation of any term in the sequence by subtracting the sum of the previous terms from the current sum. The discussion emphasizes using specific examples to clarify the process. Understanding this relationship is crucial for deriving general equations for sequences.
Aceix
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How do i go about deriving a general eqn for the nth term of a sequence provided an eqn of the sum to the nth term is given in terms of n?
 
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Rather than give you the answer, try a discrete example. Think of it this way. I know:
Sum4 = a1+a2+a3+a4
and I know
Sum3 = a1+a2+a3 .

How would I find a4 in terms of Sum4 and Sum3?
 
phyzguy said:
Rather than give you the answer, try a discrete example. Think of it this way. I know:
Sum4 = a1+a2+a3+a4
and I know
Sum3 = a1+a2+a3 .

How would I find a4 in terms of Sum4 and Sum3?
 
Does your blank reply mean you don't know?
 
phyzguy said:
Does your blank reply mean you don't know?

i meant thanks.

Aceix.
 
OK. You're welcome.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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