If the sum of the first n terms of a series is n(2n+1), then what is the nth term?

Explanation

Given the sum of n terms S_n = n(2n+1) = 2n^2 + n. The n-th term is given by T_n = S_n - S_{n-1}. Substituting gives T_n = (2n^2 + n) - (2(n-1)^2 + (n-1)) = 2n^2 + n - (2n^2 - 3n + 1) = 4n - 1.

Related questions on Algebra

• How many four-digit natural numbers are there such that <strong>ALL</strong> of the digits are odd?
• What is \sum_{r=0}^{n}2^{r}C(n,r) equal to ?
• If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) a...
• Consider the following statements : 1. If f is the subset of Z\times Z defined by f=\{(xy,x-y);x,y\in Z\}, then f is a function from...
• For how many quadratic equations, the sum of roots is equal to the product of roots?