A sequence is defined by the recurrence relation an-(p+q)an-1-(pq)an-2, where p and q-5. The first two terms of the sequence are a1=-1 and a2-2.

8. Given the recursive sequence ɑn 3. an-1 - 2· an-2, where ao = 0, a1 = 1, %3D (a) Find a2, a3, a4, a5, a6 using the recurrence relation.

Find the first five terms of the sequence defined by the following recursive definition. a, = 13 an = an-1+4, ifn>1 How is the sequence related to the sequence a, = 4n +9? ..... The first term of the sequence defined by the recursive definition is The second term of the recursive sequence is The third term of the recursive sequence is The fourth term of the recursive sequence The fifth term of the recursive sequence is How is the recursive sequence related to the sequence a, = 4n + 9? O A. The values of the sequence defined by the recursive definition are half of the values of the sequence a, = 4n + 9. O B. The values of the sequence defined by the recursive definition are greater than the values of the sequence a, = 4n + 9. OC. The values of both the sequences are the same. D. The values of the sequence defined by the recursive definition are smaller than the values of the sequence a, = 4n +9.

A sequence {an}-1 satisfies a1 = 1, a2 = 1 and n=1 4 max {am-1, an-2} – min {an-1, an-2} An = for n > 3. Select all what applies to the sequence {an}_, from the following list. (Remember: if a > b then max{a,b} = a and min {a, b} = b) n=1 (A) Divergent (B) a1014 = 1 (C) Alternating. (D) Convergent.

Please explain.

Explain each q

(a) Is the sequence {(-2)"} is a solution of the recurrence relation a, = -an-1 + 2a,-2? Show your work. (b) Is the sequence {n®2"} a solution of the recurrence relation a, = 2a,-1 – 4a,-2? Show your work. (c) Is the sequence {2(-4)" + 3} is a solution of the recurrence relation a, Aan-2?Show your work. -3an-1 +

For the infinite geometric sequence (xn) whose first four terms are:  1.3, 3.77, 10.933, 31.7057  find the values of the first term a and a common ratio r and write down a common recurrence system for this sequence.  Next, write down a closed form for this sequence and calculate the tenth term in this sequence to 3 dp

Q1. Let an = (-1)"an-1+ 2an-2, ao = 1 and a = 2. Determine the following terms of the sequence given by the above recurrence relation. (i) a2 (ii) az

The odd numbers are the numbers in the sequence 1, 3, 5, 7, 9, . . .. Define the sequence of S- numbers as follows: The first S-number is 1. The second S-number is the sum of the first S-number and the second odd number. The third S-number is the sum of the second S-number and the third odd number. The fourth S-number is the sum of the third S-number and the fourth odd number, etc., ... Compute the first seven S-numbers. Make a note of any patterns you notice. Enter the first seven S-numbers as a comma-separated list: First seven S-numbers = help (numbers)