Find the recursive formula of the following sequence. (4, 7, 15, 24, .}a1 = 4, an = a,n-1+ 3(n + 1), for n 22aa1 = 4, a, = an-1+ 3(n – 1), for n 22a1 = 4, an = a, + 3(n – 1), for n 2 2d.a1 = 4, a, = an-1+3(n – 1), for n 2 4

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Answered: Find the recursive formula of the…

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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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)
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.
List the first four terms of each sequence. An 2n + 6 : 10 12 14 ..... bn (4)" : 4 16 64 256 C1 = 5, Cn : — 2сп—1 — 3: ... .. ||
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 |
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A sequence is defined recursively by ao = 2,a1 = 3 and a, = 3a-1- 2a-2 for n 2 2. (a) Find the first five terms of this sequence. (b) Guess a formula for a,. (a non-recursive formula) (c) Find a formula for an, which involves only one preceding term.
11. Which of the following define the same Arithmetic Sequence using a Recursive Formula and an Explicit Formula? O a1 = -100, an = an-1 + 1 100 - 1(n - 1) and an %3! a, = 50, an = an-1 - 4 and a, = 50 + 4(n - 1) a, = -23, an = an-1 + 12 and an = -23 + 12(n - 1) O a1 = -41, an = an-1 + 12 and an = 12 - 41(n - 1)
2. Find the recursive formula for the following sequence: 2, 5, 10, 17, 26, ... an
Consider the sequence 1, 7, 13, 19, . . . , 6n + 7. (a) How many terms are there in the sequence? Your answer will be in terms of n. (b) What is the second-to-last term? (c) Find the sum of all the terms in the sequence, in terms of n.
For the sequence an = an–1+ an– 2 and a1 = 2, a2 = 3, %3D its first term is its second term is its third term is its fourth term is its fifth term is

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Find the recursive formula of the following sequence. (4, 7, 15, 24, . ... a1 = 4, a, = an-1+ 3(n + 1), for n 2 2 a a1 = 4, a, = an-1+ 3(n – 1), for n 2 2 a1 = 4, a, = an + 3(n – 1), for n 2 2 a1 = 4, a, = an-1+ 3(n – 1), for n 2 4