General Sequences and Series
Arithmetic Sequences
Geometric Sequences
Series
Series
100
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.
100
In an arithmetic sequence, the first term is -4 and the common difference is -1/3. What is the 10th term? The nth term?
a10=-7
an=(-1/3)n-(11/3)
100
For the given sequence, find the common ratio
1/2, 2, 8, 32, ...
r = 4
100
Find the S5
an = 2n + 1 for the first 5 terms.
35
100
Is the following a geometric series?
3 + 12 + 21 + 30, ...
No, this is arithmetic
200
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).
200
Given that a1 = 7 and the common difference is -2, find a6
a6 = -3
200
Write the formula for the given geometric sequence:
32, 16, 8, 4, ...
an = 64 (1/2) n
200
Evaluate the given series.
S10 = 365
200
Evaluate the given series:
S9 = 39,364
300
Find the sum of the following series:
2, 11, 20, 29, 38
100
300
For the given sequence, find the common difference and the 10th term.
9, 12, 15, 18, ...
d = 3
a10 = 36
300
Given that a1 = 3 and r = 2, find a6.
a6 = 96
300
The sum of the first 24 terms of the arithmetic sequence is 804. Find a24.
-1 + 2 + 5 + ...
a24=68
300
Find the sum of the first 12 terms of the geometric series:
486 + 162 + 54 + ...
S12=728.99
400
What is the next number in the pattern?
1, -1/3, 1/9, -1/27, ...
1/81
400
Find the 12th term of a sequence that has a first term of 5 and a common difference of 7
a12 = 82
400
Given the formula for the geometric sequence, list out the first 5 terms:
an = (-2)n
-2, 4,-8,16,-32
400
Evaluate the following series:
a1 = 42, an = 146, n = 14
1316
400
Find the sum of the series 9+3+1+...
27/2 or 13.5
500
Write a formula for the given sequence:
-2, 6, -18, 54, ...
an = (2/3)(-3)n
500
Write the formula for the given arithmetic sequence:
-2, 2, 6, 10, 14, ...
an = 4n - 6
500
The sixth term of a geometric sequence is 1215 and the third term is 45. Find the first term and the common ratio.
a1=5 r=3
500
Find the sum of the following series:
2 + 7 + 12 + 17 + ... 52
297
500
-425/1024 or -0.415