Let a(n) = 7, 14, 21, 28, ..., 7n,. be a sequence. Let a: N → N a) State the domain and codomain. b) Write 3 ordered pairs of the sequence. c) Explain how you know every input in the domain, n, has an output in the codomain. d) Explain how you know an input in the domain, n, cannot have two different outputs in the codomain.

2) A sequence is defined using a recursive definition as: a = 5, a, = 11, and a, = a,-1+ 2a,-2 Determine the value of a,. Show how you found your answer.

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Which recursive sequence would produce the sequence 4, 15, 59, ..? a1 = 4 and a, 5an-1 — 5 – 5 | a1 = 4 and an -5am-1 +5 ai 4 and an = = -an-1 + 4 a1 = 4 and an 4ап-1 — 1 |

22 and a17 86. Find the first term aj of the arithmetic sequence in which ag

Use S={0,2,3,4,6,9} Use D=(2,0,4,6,9,4,3,4)

Let (an) and (bn) be sequences of real numbers with the following properties:

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The graph shows the number of players in the first four rounds of the U.S Open women's singles tennis tournament. U.S. Open Women's Singles Part A: Write an explicit rule for the sequence of players in each round. fCn) f(n) 120-• (1,128) 80 • (2,64) (3,32) •(4,16)n 十+ 2 46 40 Part B: How many rounds are there in the tournament? (Hint: In the last round, only two players are left.) Round Number of players