1. What are the terms ao, a, A, and a3 of the sequence [an], where an...

  

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1. What are the terms ao, a₁, A₂, and a3 of the sequence [an], where an equals a. (n+1)(n+1) b. [n/2]+[n/2] 2. For the following questions, find a formula that generates the following sequence a₁, a2, az... [28 pts.] a. 5,9, 13, 17, 21, ... b. c. 1,0.9, 0.8, 0.7, 0.6, ... 1 1 1 1 d. '3'5'7'9'*** a. b. C. 15,20,25, 30, 35, ... 3. Describe each of the following sequence recursively. Include initial conditions and assume that the sequences begin with a₁. [21 pts.] 3, 2, 1, 0, -1, -2,... 12, 22, 32, 4², ... 1 1 1 1 2'3'4'5' 1,,, 4. Show that the sequence [an] is a solution of the recurrence relation an an-1 + 2an-2 + 2n - 9 if: = 5. Find 6. Find a. b. an = 7.2" -n+2 an = 5(-1)" - n+2 Σ, ((-2¹)-2¹) i=1 [5.5x2 = 11pts.] 3 j ΣΣ; j=1 i=1 [20 pts.] [10 pts.] [10 pts.] 1. What are the terms ao, a₁, A₂, and a3 of the sequence [an], where an equals a. (n+1)(n+1) b. [n/2]+[n/2] 2. For the following questions, find a formula that generates the following sequence a₁, a2, az... [28 pts.] a. 5,9, 13, 17, 21, ... b. c. 1,0.9, 0.8, 0.7, 0.6, ... 1 1 1 1 d. '3'5'7'9'*** a. b. C. 15,20,25, 30, 35, ... 3. Describe each of the following sequence recursively. Include initial conditions and assume that the sequences begin with a₁. [21 pts.] 3, 2, 1, 0, -1, -2,... 12, 22, 32, 4², ... 1 1 1 1 2'3'4'5' 1,,, 4. Show that the sequence [an] is a solution of the recurrence relation an an-1 + 2an-2 + 2n - 9 if: = 5. Find 6. Find a. b. an = 7.2" -n+2 an = 5(-1)" - n+2 Σ, ((-2¹)-2¹) i=1 [5.5x2 = 11pts.] 3 j ΣΣ; j=1 i=1 [20 pts.] [10 pts.] [10 pts.]