(a) What are the 5th terms for each sequence? That is, what are the values of a, and b5? (b) For some real numbers p and q, bn = p · (an) + q · (-1)" for all n > 1. (You do not need to show this.) What are the values of p and q?
(a) What are the 5th terms for each sequence? That is, what are the values of a, and b5? (b) For some real numbers p and q, bn = p · (an) + q · (-1)" for all n > 1. (You do not need to show this.) What are the values of p and q?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Hello there, Im studying for exams and I cant solve this problem for a long time. Please show all steps so I can learn.
I will give a like
Transcribed Image Text:The sequence A, with terms a1, a2, a3, . .., is defined by
an = 2", for n >1.
The sequence B, with terms b1, b2, b3, ..., is defined by
bị = 1, b2 = 1, and b, = bn-1+2b,–2; for n > 3.
For example, b3 = b2 + 2b1 = 1+2(1) = 3.
In this question, the following facts may be helpful:
• A geometric sequence is a sequence in which each term after the first is obtained
from the previous term by multiplying it by a non-zero constant called the common
ratio. For example, 3,6, 12 is a geometric sequence with three terms and common
ratio 2.
• The sum of the first n terms of a geometric sequence with first term a, and common
ratio r + 1, equals a ( ).
Transcribed Image Text:(a) What are the 5th terms for each sequence? That is, what are the values of as
and b;?
(b) For some real numbers p and q, bn = p · (an) + q · (-1)" for all n > 1. (You do
not need to show this.) What are the values of p and q?
%3D
That is,
(c) Let S, be the sum of the first n
Sn = bị + b2 + b3 + · ··
terms in sequence B.
+ bn. Determine the smallest positive integer n that
satisfies S, 2 162021.
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