5.4 Sum of Arithmetic Series (1/4)

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5.4 Sum of Arithmetic Series (1/4) Sn = (a + l) n 2 Sum (add) to n terms Last (or nth Term) Term Position First Term a+(n-1)d Sn = n/2(a + a+(n-1)d) Sn = [2a+(n-1)d] n 2

5.4 Sum of Arithmetic Series (2/4) Sn = (a + l) n 2 Use If you know or are asked to find ‘l’ Use Sn = [2a+(n-1)d] n 2 If you don’t know and are not asked to find ‘l’

5.4 Sum of Arithmetic Series (3/4) Sum the first 30 terms of the series 12 + 14 + 16 + … a = 12 n = 30 d = 2 Sn = n/2(2a +(n-1)d) S30 = 30/2x(2x12 +(30-1)x2) = 1260

5.4 Sum of Arithmetic Series (4/4) Sum the series 8 + 12 + 16 + … + 100 Find n. a = 8 d = 4 n = 24 l = 100 a = 8 d = 4 Sn = n/2(a + l) Tn = a +(n-1)d S24 = 24/2(8 + 100) 100 = 8 +(n-1)x4 100 = 8 + 4n - 4 100 = 4n + 4 = 1296 4n = 96 n = 24