An arithmetic series is defined by its first term a a\,a and common difference ddd. Prove that the sum of the first n n\,n terms is given by the formula:
Sn=n2[2a+(n−1)d] S_n = \frac{n}{2}[2a + (n-1)d] Sn=2n[2a+(n−1)d]A model for the hourly energy output, EkE_kEk (in Joules), of a pulsing laboratory generator during the kkk-th hour is given by:
Ek=7k+3(−1)k E_k = 7k + 3(-1)^k Ek=7k+3(−1)kDetermine the value of: E12E_{12}E12
∑k=161Ek\sum_{k=1}^{61} E_k∑k=161Ek
