Sequences
Arithmetic Sequences and Series
Geometric Sequences and Series
Binomial Theorem
What kind of sequence is it?
100
Find the first 5 terms of the sequence:
{an} = { 4n - 3 }
1, 5, 9, 13, 17
100
Find the common difference and the first 5 terms of the following arithmetic sequence:
{a_n} = {16 - 1/2n }
d = -1/2 ; a_1 = 15.5, a_2= 15, a_3 = 14.5, a_4 = 14, a_5 = 13.5
100
Find the sum:
sum_(k=1)^10 (-2)^k
682
100
Expand and simplify: (x + 1)3
x3 + 3x2 + 3x + 1
100
Is the following sequence arithmetic, geometric, or neither?
{an} = { 2n }
arithmetic
200
Express the following sum using summation notation:
1 + 2 + 3 + 4 + ... + 25
sum_(k=1)^25 k
200
Find the 80th term of: 5, 0 , -5, ...
-390
200
Find the 10th term of the geometric sequence:
1, -2, 4, ...
-512
200
Expand and simplify: (2x + 3)4
16x4 + 96x3 + 216x2 + 216x + 81
200
Is the following sequence arithmetic, geometric, or neither?
{an} = { 2n }
geometric
300
Find the sum of:
sum_(k=1)^36 5
36*5 = 180
300
Find the sum of: 5 + 9 + 13 + ... + 49
324
300
Find the nth term formula of a geometric sequence whose 3rd term is 100 and 6th term is 12.5. Make sure to simplify your final answer.
{ a_n } = { 400(1/2)^(n-1) }
300
Expand and simplify: (x2 + 5y)3
x6 + 15x4y + 75x2y2 + 125y3
300
Is the following sequence arithmetic, geometric, or neither?
{an} = { n2 - 1 }
neither
400
Find the nth term of the sequence:
1, -2, 3, -4, 5, -6, ...
a_n = n(-1)^(n-1)
400
Find the nth term formula of an arithmetic sequence whose 5th term is -2 and 13th term is 30. Make sure to simplify your final answer.
{a_n} = { 4n - 22 }
400
Determine if the following infinite geometric series converges or diverges. If it converges, find its sum.
2 - 1 + 1/2 - 1/4 + ...
converges
S_\infty = 4/3
400
Expand and simplify: (2x2 - y2)5
32x10 - 80x8y2 + 80x6y4 - 40x4y6 + 10x2y8 - y10
400
Is the following sequence arithmetic, geometric, or neither?
12, 6, 3, 1.5, ...
geometric
500
A colony of rabbits begins with one pair of mature rabbits, which produce a pair of offspring (one male, one female) each month. Assume all rabbits mature in 1 month and produce a pair of offspring (one male, one female) after 2 months. If no rabbits ever die, how many pairs of mature rabbits are there after 7 months?
42 mature rabbit pairs
500
An outdoor amphitheater has 35 seats in the first row, 37 in the second row, 39 in the third row, and so on. There are 27 rows altogether. How many people can the amphitheater seat?
1,647 seats/people
500
Find x so that x + 2, x + 3, and x + 5 are consecutive terms (in that order) of a geometric sequence.
x = -1
500
Find the 5th term of (3x2 - 4y2)7
241,920x6y8
500
Is the following sequence arithmetic, geometric, or neither?
2/3, 3/4, 4/5, 5/6, ...
neither