Sequences, Series and Summations -- Section 8.2 --

 Sequence: a function whose domain is the set of natural numbers. natural numbers (counting numbers) {1, 2, 3, 4...} Series: is a sum of a sequence. Write the first five terms of the sequence.   an = 2n2 - n
 Solve Step a1 = 2(1)2 - 1 = 2(1) - 1 = 2 - 1 = 1 Start with n = 1 a2 = 2(2)2 - 2 = 2(4) - 2 = 8 - 2 = 6 n = 2 a3 = 2(3)2 - 3 = 2(9) - 3 = 18 - 3 = 15 n = 3 a4 = 2(4)2 - 4 = 2(16) - 4 = 32 - 4 = 28 n = 4 a5 = 2(5)2 - 5 = 2(25) - 5 = 50 - 5 = 45 n = 5 The first five terms are 1, 6, 15, 28, 45 an = 2n2 - n  can also be written as  f(n) = 2n2 - n .  The term an indicates it is a special function called a sequence.  Write the first five terms of the sequence.   an = n2 + 3n [Solution]  Evaluate the sum. We add the first five terms of the sequence an = 2n2 - n   from example 1. Solve Step The first five terms are 1, 6, 15, 28, 45 =  1 + 6 + 15 + 28 + 45 = 95 n = 1 means start at 1 5 means end at 5.  Evaluate the sum.  [Solution]  Evaluate the sum. Solve Step K = 3 means start at 3 5 means end at 5. k = 3, 4, 5 Add the fractions The sum of a sequence is called a series.  Evaluate the sum.  [Solution] Tutorials and Applets by
Joe McDonald