Vocabulary
Arithmetic, Geometric or Neither? State the common difference or common ratio if there is one.
5, 10, 15, 20,...
Arithmetic
d = 5
Find the common difference, then state the rule.
-2, 2, 6, 10, 14, ...
d = 4
an = 4(n-1) - 2
For the given sequence, find the common ratio
1/2, 2, 8, 32, ...
r = 4
Find the sum of the arithmetic sequence given:
a1 = 4, a10 = 22, n = 10
S10 = 130
Arithmetic, Geometric or Neither? State the common difference or common ratio if there is one.
2, 10, 50, 250,...
Geometric
r = 5
For the given sequence, find the common difference and the 10th term.
9, 12, 15, 18, ...
d = 3
a10 = 36
For the given geometric sequence, find the common ratio:
125, 25, 5, 1,...
r = 1/5
Find the sum of the geometric sequence given:
2 + 8 + 32 + 128 ... n = 8
Sn = 43690
What is the difference between an arithmetic and a geometric sequence?
An arithmetic sequence is a sequence that has a common difference (the same number gets added each time).
A geometric sequence is a sequence that has a common ratio (the same number gets multiplied each time).
Arithmetic, Geometric or Neither? State the common difference or common ratio if there is one.
-1, 4, 10, 17, 25,...
Neither
For the given sequence, find the common difference and the 15th term.
−3, −23, −43, −63, ...
d = -20
a15 = -283
Given that a1 = 3 and r = 2, find a6.
a6 = 96
Find the sum of the arithmetic sequence given:
20 + 30 + 40 + 50..., n = 15
Sn = 1350
Arithmetic, Geometric or Neither? State the common difference or common ratio if there is one.
-16, -12, -8, -4,...
Arithmetic
d = 4
Given that a1 = 7 and the common difference is -2, find a6
a6 = -3
Write the formula for the given geometric sequence:
32, 16, 8, 4, ...
an = 32 (1/2) n-1
Find the sum of the geometric sequence given:
-3 + 15 - 75 + 375 ... n = 8
Sn= 195312
What is the difference between a sequence and a series?
A sequence is an ordered list of numbers, whereas a series is the sum of a given number of terms in a sequence.
Arithmetic, Geometric or Neither? State the common difference or common ratio if there is one.
−2.5, 10, −40, 160, −640
Geometric
d = -4
For the given sequence, find the common difference and the 15th term.
−34, −64, −94, −124, ...
d = -30
a15 = -454
For the given geometric sequence, find the common ratio and then find the 8th term.
−1, 6, −36, 216, ...
r = -6
a8 = 279,936
Find the sum of the arithmetic sequence given:
20 + 27 + 34 + 41..., n = 16
S16 = 1160