# Arithmetic sequence geometric sequence recurrence sequence

Not what you're looking for?

1) Consider the sequence given by: U1 = 3.9, un+1 = un - 1.7 (n = 1,2,3,...).

i) What type of sequence is this?

ii) Please write the first four terms of the sequence.

iii) Find a closed form for the sequence.

iv) Use the closed form from 1. iii to find the value of n when un = -76

2) Consider the following geometric sequence.

400, 320, 256, 204.8, ...

i) Write down a recurrence system that describes this sequence.

(Denote the sequence by Xn, and its first term by x1.)

ii) Find a closed form for this sequence.

iii) Use the closed form part 2ii to find the tenth term of the sequence to four decimal places.

3) Consider the linear recurrence sequence

X1 = 23, xn+1 = 1.3xn - 12 (n = 1,2,3,...).

i) Find a closed form for the sequence.

ii) Use the closed form to find the eighth term of the sequence, correct to four significant figures.

iii) Describe the long-term behaviour of the sequence.

##### Purchase this Solution

##### Solution Summary

Three problems with several sub categories on arithmetic sequence, geometric sequence and recurrence sequence have been answered. I have provided very clear, step by step solution so that the student will understand the technique to solve similar problems in the future. Please download them as these are wonderful sample questions and answers on sequences and series.

##### Solution Preview

Following is the text part of the solution. Please see the attached file for complete solution. Equations, diagrams, graphs and special characters will not appear correctly here. Thank you for using Brainmass.

===============================================================================

Answers:

(1)

i. Arithmetic sequence

ii. u1 = 3.9, u2 = 2.2, u3 = 0.5, u4 = -1.2

iii.

u2 = u1 - 1.7

u3 = u2 - 1.7 = u1 - 1.7- 1.7 = u1 - 2(1.7)

This pattern continues, and we can write the nth term as,

un = 3.9 - (n-1) *1.7

iv.

un = -76 = u1 - (n-1) * 1.7

-76 = 3.9 - (n-1) * 1.7

Solve for n:

n = ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Probability Quiz

Some questions on probability

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.