Algebra 1
arithmetic sequences
1.
Copy the first 3 squares on graph paper, then follow the pattern and
draw the next 3 squares.
2.
Copy the table and fill in the blanks.
square number (n)
shaded (s)
unshaded (u)
1
1
0
2
3
1
3
5
4
4
5
6
3.
What is the difference between each number in the set of shaded
areas? What is the difference between each number in the set of
unshaded areas?
4.
Which set had the same difference between each number? What was
that common difference (d)?
5.
A NOW-NEXT equation is written in the form:
Next=Now + (common difference) or, symbolically: sn+1=sn+d
Write a NOW-NEXT equation for the shaded area.
6.
It is important to know where the sequence starts, called the zero-th
term. To find the 0-th term, subtract the common difference from the
1st term. What is the 0-th term for the shaded areas?
7.
The equation with variables s and n would be written:
s=(common difference)n+(0-th term)
Write the equation for the shaded area in terms of s and n.