Proportional relations and arithmetic sequences.

1. What's Wrong With
This Picture?
SMALL is the new big by flickr user assbach

2. INTERPOLATION & EXTRAPOLATION
HOMEWORK
A student in electronics measured the current through a circuit
with a constant resistance while the voltage was increased. The
results are shown below, with the voltage measured in volts and
the current in milliamps.
a) Make a scatterplot of the data. Set the window to show the origin
(0, 0) and the x-and y-axes.
b) What is the equation for a line of best fit? (Use three decimal
places)
c) Rewrite the equation, using the voltage as, V, and the current as, I.
d) What is the slope of the line? INTE
RPO
LAT
ION
e) What would be the current if the voltage were 8.000 volts?
EXTR
APOL
f) What would be the current if the voltage were 22.736 volts? ATIO
N

3. INTERPOLATION & EXTRAPOLATION
a) Make a scatterplot of the data.
Set the window to show the origin
(0, 0) and the x-and y-axes.
b) What is the equation for a line of
best fit? (Use three decimal places)
c) Rewrite the equation, using the
voltage as, V, and the current as, I.
d) What is the slope of the line?

4. INTERPOLATION & EXTRAPOLATION
INTE
RPO
LAT
e) What would be the current if the voltage were 8.000 volts? ION
EXTR
APOL
ATIO
f) What would be the current if the voltage were 22.736 volts? N
22.736 22.736

5. In an experiment, the following masses were attached to
a spring. As they were attached, the following elongations
were recorded: HOMEWORK
1. What is the independent variable?
2. Use your graphing calculator to
plot the elongation against mass.
3. Use your calculator to find a regression line (line
of best fit) for the data. What is the y-intercept?
4. Select two points in the table and use
them to calculate the slope of the line.
5. Is it the same in the equation of the line?
6. Do you think that this model for the elongation of the
spring is always accurate? What do you think would
happen if the mass were increases to 15 kg?

6. Jimmy has observed that the distance to a thunderstorm can be
estimated by counting the number of seconds between a flash of
lightning and the sound of the thunder. With further investigation, he
obtains the following information:
a. Complete the pattern shown in the chart up to
21 seconds.
b. Graph the information using t as the
independent variable and d as the dependent
variable.
c. What is the equation for this direct proportion?
What is the constant of proportionality? This can
be calculated in the same way as the slope of a
line.
d. Estimate the distance if the time is 10 seconds,
20 seconds, 30 seconds.

7. Find the next three terms in each sequence of numbers ...
4, 7, 10, 13, , ,
3, 6, 12, 24, , ,
32, 16, 8, 4, , ,
1, 1, 2, 3, 5, 8,13, , ,

8. 4, 7, 10, 13, , ,

9. Some Definitions
Sequence: An ordered list of numbers that follow a certain pattern (or rule).
Arithmetic Sequence:(i) Recursive Definition: An ordered list of numbers
generated by continuously adding a value (the common
difference) to a given first term.
(ii) Implicit Definition: An ordered list of numbers where
each number in the list is generated by a linear equation.
Common Difference (d):(i) The number that is repeatedly added to
successive terms in an arithmetic sequence.
(ii) From the implicit definition, d is the slope of the linear
equation.

10. To Find The Common Difference
d is the common difference d = tn - t(n - 1)
tn is an arbitrary term in the sequence
t(n - 1) is the term immediately before tn in the sequence
To Find the nth Term In an Arithmetic Sequence
tn is the nth term tn = a + (n - 1)d
a is the first term
n is the quot;rankquot; of the nth term in the sequence
d is the common difference
Example: Find the 51st term (t51) of the sequence 11, 5, -1, -7, ...
Solution: a = 11 t51 = 11 + (51 - 1)(-6) Implicitly
d = 5 - 11 t51 = 11 + (50)(-6)
= -6 t51 = 11 - 300
n = 51 t51 = -289

11. Which of the following sequences are arithmetic sequences?
a) 1, 2, 6, 24, 120,… HOMEWORK
b) 3, 9, 15, …
c) 2, 4, 8, 16, 32,…
d) 1, 2, 3, 5, 8, 13, …
e) -4, -1, 2, 5, 8,…

12. What is the pattern in the sequence 2, 8, 14, 20, 26…?
Suggest an equation that could be used to generate such a list.
HOMEWORK

13. a) Why do the numbers 5, 8, 11, 14, 17… form an arithmetic
sequence?
HOMEWORK
b) What is the defining equation that produced them?
c) What is the 27th term of this sequence?