General Ideas
How I Met Your Common Difference
Game of Ratios
Sumthing Special
What the Sigma?
100
What is the difference between a sequence and a series?
A sequence is an ordered list of numbers (commas), whereas a series is the sum of a given number of terms in a sequence (addition signs).
100
Write an explicit rule for the given arithmetic sequence:
{-2, 2, 6, 10, 14, ...}
an = 4n - 6
100
For the given sequence, find the common ratio
{1/2, 2, 8, 32, ...}
r = 4
100
Find the sum for 5 terms of the series given the following:
an = 2n + 1
S5 = 35
100
Determine if the following series is arithmetic or geometric and state why.
3 + 12 + 21 + 30, ...
Arithmetic, each term is 9 greater than the previous - meaning we're adding not multiplying
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 explicit rule for the given geometric sequence:
{32, 16, 8, 4, ...}
an = 32 (1/2) n-1
200
Find the sum of the first 13 terms of the arithmetic series with the rule an = 3n - 5.
S13 = 208
200
Determine if the following series is arithmetic or geometric and state why.
3 + 12 + 48 + 192 + ...
Geometric, each term is 4 times the previous - meaning we're multiplying not adding
300
Find the sum of the following sequence:
{2, 11, 20, 29, 38}
100
300
For the given sequence, find the common difference/ratio 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
S = 728
400
Write the recursive rule for the following sequence:
30, 25, 20, 15, 10, ...
an = an - 1 - 5
400
Find the 12th term of a sequence that has a first term of 5 and a common difference of 7
a12 = 82
400
Write the explicit formula for the following:
a1 = 5 ; an = 3an-1
an = 5 (3)n-1
400
Find the sum of the following series:
a1 = 42, a14 = 146, n = 14
S14 = 1316
400
Evaluate the given series:
S9 = 39,364
500
Write an explicit rule for the given sequence:
{-2, 6, -18, 54, ...}
an = -2(-3)n-1
500
Find the sum of the following series:
{2 + 7 + 12 + 17 + ... + 52}
297
500
Write the explicit rule if the sequence is geometric and find a11
2, 8, . . .
an = 2(4)n-1
a11 = 2097152
500
Evaluate the given series.
S10 = 365
500
The sum of the series from term 1 to term 45 with the rule:
8 - 3i
S = -2,745