9.1 Sequences and Series

A sequence is a collection of numbers that are ordered. Ex. 1, 3, 5, 7, …. Finding the terms of a sequence. Find the first 4 terms of the sequence whose nth term is a n = 3n - 2 a 1 = 1 a 2 = 4 a 3 = 7 a 4 = 10

Find the first 4 terms of a n = 3 + (-1) n Write an expression for the nth term for each of the following sequences. 1, 3, 5, 7, … 2, 5, 10, 17, … a n = 2n - 1 a n = n , 4, 2, 4 Multiples: n, 2n, 3n Powers: n 2, n 3, 2 n, 3 n Assignment: odd, all, odd

Factorial = n 4 1 = 28

Write the first five terms of the sequence defined recursively a 1 = 15, a k+1 = a k + 3 a 1 = 15 a 2 = a 1+1 = a 1 +3 = 18 a 3 = a 2+1 = a 2 +3 = 21 a 4 = 24 a 5 = 27

Summation Notation Ex. 3(1) + 3(2) + 3(3) + 3(4) + 3(5) = = 8 = = 90 i0i0

Write the sum of the sequence in sigma notation. Hw odd or