General Sequences and Series
Arithmetic Sequences
Geometric Sequences
Arithmetic Series
Geometric 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
A theater has 32 rows of seats. If there are 26 seats in the 1st row, 30 in the 2nd, 34 in the 3rd, and so on, how many seats are there in all? Assume the pattern continues.
2816 seats
100
For the given sequence, find the common ratio
1/2, 2, 8, 32, ...
r = 4
100
Find the summation of this series:
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
Find the 7th term in the following sequence: 6, 18, 54, 162, …
4,374
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
Determine the number of terms in the series:
-1 + 2 + 5 + ... + 68
n = 24
300
Find the sum of the geometric series:
486 + 162 + 54 + ... + 2
728
400
What is the a14 of the sequence 360, 356, 352, ...
308
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
-1/2, 1/4, -1/8, 1/16, -1/32
400
Evaluate the following series:
a1 = 42, an = 146, n = 14
1316
400
Find the sum of the first 8 terms of the geometric sequence:
2,6,18,54,…
6,560
500
Find the 112 term of the sequence 4, 7, 10, 13, ...
337
500
Find the 2nd and 3rd term of the sequence –1, ___, ___, 56, 75, ...
18, 37
500
What is a possible value for the missing term of the geometric sequence?
33, ___, 1188, ...
198
500
Find the sum of the following series:
2 + 7 + 12 + 17 + ... 52
297
500
-425/1024 or 0.415