- #1
Aceix
- 49
- 1
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?
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?
phyzguy said:Does your blank reply mean you don't know?
The formula for finding the nth term of a sequence is an = a1 + (n-1)d, where a1 is the first term in the sequence, n is the term number, and d is the common difference between terms.
In order to identify the pattern in a sequence, you should look for a consistent difference or ratio between terms. Once you have identified the pattern, you can use the formula an = a1 + (n-1)d to find the nth term.
Yes, the nth term of a sequence can be negative. This can occur if the common difference is a negative number or if the first term in the sequence is a negative number.
No, not all sequences have a pattern or an nth term. Some sequences may be random or have a complex pattern that is difficult to identify. In these cases, there may not be a simple formula to find the nth term.
The formula an = a1 + (n-1)d can be used for arithmetic and geometric sequences, which have a constant difference or ratio between terms. However, this formula may not apply to other types of sequences, such as Fibonacci or alternating sequences.