- #1
Superposed_Cat
- 388
- 5
Hi all, given the sum of a series and a single term how would one find the nth term? Any help appreciated.
To find the value of Tn, you can use the formula Tn = Sn - Sn-1, where Sn is the sum of the first n terms of the series and Sn-1 is the sum of the first n-1 terms. This formula works for both arithmetic and geometric series.
Yes, Tn can be negative depending on the values of the series and term. If the series is decreasing or the term is a negative number, then Tn can be negative.
If the series does not have a specific pattern, then it may not be possible to find a general formula for Tn. In this case, you may need to calculate Tn manually by adding the terms in the series until you reach the desired term.
Yes, Tn and Sn represent different values. Tn is the value of a specific term in a series, while Sn is the sum of a certain number of terms in a series. Tn can be calculated using the formula Tn = Sn - Sn-1, where Sn is the sum of the first n terms of the series and Sn-1 is the sum of the first n-1 terms.
Yes, Tn can be a decimal or a fraction depending on the values of the series and term. For example, in a geometric series with a common ratio between 0 and 1, Tn can be a fraction. In an arithmetic series, Tn can be a decimal if the common difference is not a whole number.