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 The sequence A, with terms a1, a2, a3, . .., is defined byan = 2", for n >1.The sequence B, with terms b1, b2, b3, ..., is defined bybị = 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 obtainedfrom the previous term by multiplying it by a non-zero constant called the commonratio. For example, 3,6, 12 is a geometric sequence with three terms and commonratio 2.• The sum of the first n terms of a geometric sequence with first term a, and commonratio r + 1, equals a ( ). (a) What are the 5th terms for each sequence? That is, what are the values of asand b;?(b) For some real numbers p and q, bn = p · (an) + q · (-1)" for all n > 1. (You donot need to show this.) What are the values of p and q?%3DThat is,(c) Let S, be the sum of the first nSn = bị + b2 + b3 + · ··terms in sequence B.+ bn. Determine the smallest positive integer n thatsatisfies S, 2 162021.

Answered: Image /qna-images/answer/f55da872-4e7e-46e3-891e-5a32602e4180.jpg

(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?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.1: Sequences And Their Notations

Problem 70SE: Calculate the first eight terms of the sequences an=(n+2)!(n1)! and bn=n3+3n32n , and then make a...

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

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

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 ( ).

(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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