2Ex 1Start with a square with sides 1 unit long. On the right side, add on a square of the same size. Continue adding one square at a time in this way. Draw the first four figures.
3Ex 2Write the number of 1 unit segments in each figure from ex 1 as a sequence.
4Ex 3Describe the pattern formed and find the next three terms. 243, 81, 27, 9, …
5Ex 4Suppose you drop a ball from a height of 100 cm. It bounces back to 80% of its previous height. How high will it go after its fifth bounce?
6We can use a variable with positive integer subscripts to represent the terms in a sequence: a1 a2 a3 – first, second and third termsan-1: n – 1 terman : nth terman+1 : n + 1 termn is the term number
7Recursive formulaDefines the terms in a sequence by relating each term to the ones before it. (ex 4 was recursive b/c the height was 80% of its previous height)Formula would be an = 0.80an-1 wherea1 = 100
8Ex 5 Describe the pattern of the sequence: 2, 6, 18, 54, 162, … Write a recursive function.Find the 6th and 7th terms.Find the value of a10
9Explicit formula Expresses the nth term in terms of n Finding the value of a term without knowing the preceding term.(Find a link between the term number and the term value.)