Number Patterns

Arithmetic Sequences

100

Write the next three terms:

-7, -14, -21, -28

-35, -42, -49

200

Would the following ordered pairs represent an arithmetic sequence? Explain. 

(1, 2), (2,4), (3,7), (4, 11)

No, the y-values do not share a common difference.

or 

No, the points would not form a line.

300

Write the general formula to find the nth term of the following sequence.  Provide in both explicit and linear form.

u₄ = 1

u₅ = 5

u₆ = 9

u_n= -11+ 4(n-1)

and

u_n= -4n -15

400

The 3rd term of a linear sequence is ⅔.  The 8th term is -2 ⅚ .  Find the common difference.

d = -7/10

500

The 23rd term of a linear sequence is -8.  The 27th term is -30.  Find the general formula to find the nth term of the sequence.

u_n=113 - 5.5(n - 1)

Geometric Sequences

100

Write the next three terms of the geometric sequence:

64, -16, 4, -1

1/4, -1/16, 1/64

200

Write a general formula for the nth term of the geometric sequence:

4, 10, 25, 62.5

u_n= 4 (5/2)^n-1

300

You are given the 2nd and 5th term of a geometric sequence, find the common ratio.

u₂= -5

u₅= 320

r = -4

400

A sheet of paper is 0.1 mm thick.  A machine folds the paper in half, once, twice, three times, and so on.

Your friend makes the statement, "If it were possible for the machine to fold the paper in half 16 times, it would be taller than you."

Is this statement true?  Justify your response.

The general formula of this geometric sequence is

u_n= 0.1 (2)^n-1

u₁₆= 0.1 (2)^n-1=3276.8 mm or 3.2768 meters

The tallest person in the world recorded was less than 3 meters tall. Yes, the friend's statement is true.  

500

You are given the following terms of a geometric sequence:

u₃=2/3 and u₅=3/2

Write the general formula to find the nth term

u_n = (8/27)(3/2)^n-1

Quadratic Sequences

100

Find the first 4 terms of the sequence:

6n - n²

5, 8, 9, 8, 5

200

Is this a quadratic sequence?  Justify.

25, 8, 1, 4, 17

Yes, there is a common 2nd difference of 10

300

What is the "b" value of the following quadratic sequence?

−4,    −12,    −24,    −40,    −60

 b = -2

400

A    sequence    has    an    nth    term    of        

n²    −    6n    +    7              

Work    out    which    term    in    the    sequence   has    a    value    of    23.

n = 8

500

What is the general formula of the following quadratic sequence?

100,    96,    90,    82,    72    …    

u_n= -n² - n + 102

Miscellaneous

100

Can -8 be part of the following arithmetic sequence?

un = 12 + .5(n - 1)

No, n = -39 and the term number must be a whole number.  Negative numbers are not whole numbers.

200

The    nth    term    of    a    quadratic    sequence  is    n²    +    4n.              

Two consecutive  terms  have  a  difference of 25.       

Work out the two terms.    

140 and 165

300

The    first    4    terms    of    a    sequence    are:        400,    390,    375,    355    …              

Which    term    is    the    first    to    be    negative?    

The 13th term, which is -50.

400

The following two consecutive terms are part of a geometric sequence.  Find the common ratio.

4√2, 16

r = √8

500

The    first    5    terms    of    a    quadratic    sequence    are:        

4,    10,    18,    28,    40              

Work    out    the    difference    between    the    10th and    20th    terms.    

330