sequences, that is: an-c1r-1+c2r2-1, where c1 and c2 still need to bedetermined- to determine the constants c1 and c2, use the starting values a and a2givenabove to set up a system of 2 equations for the 2 values c1 and c2- finally, solve the system of 2 equations to determine c1 and c2Put all the parts together and you should now have a closed formula for thesequence in the form a,=cr,n-1+cr2n-1, where the growth rates r and r2 and theconstants C and c2 are all known values.C2To verify that you have correctly solved this recurrence relation and constructed thecorrect closed formula, in the box below enter the ratio of the 2 constants cl(If your answer is a decimal, round it correctly to 4 decimal places.)Answer: A sequence is defined by the recurrence relation an-(p+q)an-1-(pq)an-2, where p-D4and q=5. The first two terms of the sequence are a1=-1 and a2=2.To determine a closed formula for the terms of the sequence, we can follow theprocedure we discussed in class:• substitute a geometric sequence an=rn-1 into the recurrence relation (and alsosubstitute appropriately adjusted expressions for an-1 and an-2)• collect all the terms onto one side of the equation and factor out a commonfactor of rn-3• solve the resulting quadratic equation to get 2 possible geometric growthrates, r, and r2• our closed formula must therefore be be some combination of 2 geometricsequences, that is: a,=c1r1"-1+c2r2 c1 and c2 still need to ben-1 where

Given: A recurrence relation, an=p+qan-1-pqan-2, where p=4, q=5, a1=-1 and a2=2. To find: Solution…

Answered: A sequence is defined by the recurrence…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please explain.
Explain each q
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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)

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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.