Math II UNIT QUESTION: How is a geometric sequence like an exponential function? Standard: MM2A2, MM2A3 Today’s Question: How do you recognize and write rules for number patterns? Standard: MM2A3d

Section 4.7 Sequences & Series

Sequence A sequence is a set of numbers in a specific order Infinite sequence Finite sequence

Sequences – sets of numbers

Ex. 1 Find the first four terms of the sequence First term Second term Third term Fourth term

Ex. 2 Find the first four terms of the sequence

Writing Rules for Sequences We can calculate as many terms as we want as long as we know the rule or equation for a n. Example: 3, 5, 7, 9, ___, ___,……. _____. a n = 2n + 1

Writing Rules for Sequences Try these!!! 3, 6, 9, 12, ___, ___,……. _____. 1/1, 1/3, 1/5, 1/7, ___, ___,……. _____. a n = 3n, a n = 1/(2n-1)

Series – the sum of a certain number of terms of a sequence “Add up the terms in the sequence beginning at term number 1 and going through term number “n”. Start Stop Formula

Infinite Sequence Infinite Series Finite Seriesor nth Partial Sum

SUMMATION NOTATION Lower limit of summation (Starting point) Upper limit of summation (Ending point) Sum of the terms of a finite sequence

If you have a constant you can pull it out in front FIRST Ex 7

Ex 7b

Homework Page 135 #2-16 (even), 22-24, 26