# Arithmetic Sequence

A company decides to fine it workers for parking violations on its property. The first offense carries a fine of $25.00 the second offense is $30.00 the third offense is $35.00 and so on. what is the fine for the eight offense? Please show your work and whether you use arithmetic sequence or a geometric sequence and use the proper formulas where applicable. Be concise in your reasoning .

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Answer

The first offense carries a fine of $25.00

The second offense carries a fine of $30.00

The third offense carries a fine of $35.00 and so on.

Clearly ...

#### Solution Summary

The solution provides step by step method for the calculation of arithmetic progression. Formula for the calculation and Interpretations of the results are also included.

Several questions on arithmetic sequence, geometric sequence and recurrence sequence.

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.