Arithmetic
Geometric
Sigma Notation
More Sequences and Series
Miscellaneous
100
Provide the first 3 terms of a_n=6(n-1)+10
10, 16, 22
100
Provide the first three terms of
a_n=3(-5)^{n-1}
3, -15, 75
100
Evaluate
\sum_{n=1}^5n(n+2)
85
100
How many terms of a_n are used to calculate
\sum_{n=8}^{105}a_n
108 terms
100
Evaluate 4-4(0)
4
200
Recursively define 61, 53, 45, ...
a_n=a_{n-1}-8
a_1=61
200
Recursively define
11, 22/7, 44/49, 88/343, ...
a_n=a_{n-1}\cdot 2/7
a_1=11
200
Write sigma notation from the following series 5, 5/6, 5/36, 5/216, 5/1296 (no-calc)
\sum_{n=1}^{5}5(\frac{1}{6})^{n-1}
\sum_{n=1}^{5}30(\frac{1}{6})^{n}
\sum_{n=0}^{4}5(\frac{1}{6})^{n}
200
Create the equation (explicit or recursive):
12, 27, 48, 75, ...
a_n=3(n+1)^2
200
Expand (5x+\sqrt{3y})^2
25x^2+10x\sqrt{3y}+3y
300
What is the 5th term of the sequence
a_n=6(n-5)+35
a_5=35
300
What is the 10th term (leave answer as a power, no need to evaluate all the way) of the sequence defined by
a_{n+1}=a_n\cdot -3, a_3=-7
a_10=-7(-3)^7=15309
a_10=(-7/9)(-3)^9
a_10=(7/27)(-3)^10
300
Solve the equation (round to 3 decimal places)
(\sum_{n=3}^5\log(n-1))x=100
x\approx72.453
300
\sum_{n=1}^{419}3n-5=261875
What is \sum_{n=1}^{420}3n-5 ?
263130
300
Sketch the graph of S_k vs
k for the series S_k=\sum_{n=1}^kn
400
What is the 10th term of the arithmetic sequence where a_1=13 and a_21=153?
a_10=76
400
Determine the common ratio a_n=3^{n+2}\cdot2^{3-2n}
r=3/4
400
What is the 4th partial sum of
a_n=(a_{n-1})/(n), a_1=4 ?
S_4=4+2+2/3+2/12=41/6
400
Represent the sum below using sigma notation:
3/5-4/25+5/125-6/625, ...
\sum_{n=1}^4(-1)^{n-1}(n+2)/5^n
400
Sketch the graph of S_k vs
k for the series S_k=\sum_{n=1}^k(1/2)^{n-1}
500
Is 349765 a term in the arithmetic sequence where t_1=13 and d=5 ?
No
500
Is -170 2/3 a term in the geometric sequence where
t_1=1/3 and r=-2 ? If so, what term is it?
Yes
t_10=170 2/3
500
Evaluate \sum_{n=1}^{10}1/n-1/(n+1)
S_10=9/10
500
What is the sum of the first k odd numbers?
\sum_{n=1}^{k}2n-1=k^2
500
Find the next two terms ( a_13 and a_14 ) of the sequence:
1, 11, 21, 1112, 3112, 211213, 312213, 212223, 114213, 31121314, 41122314, 31221324, ____, ____
21322314, 21322314