Intro to Sequences
Provide the first three terms of the sequence:
an=2n+2
a1=2(1)+2=4
a2=2(2)+2=6
a3=2(3)+2=8
4,6,8
The first term of an arithmetic sequence is a1=5, and the common difference is d=4. What is the 6th term?
a6=5+(6-1)x4=25
The first term of a geometric sequence is 3, and the common ratio is 2. What is the 5th term?
a5=48
n=1
k=5
x=4
20
Find the sum of the infinite series:
n=0
x=(1/2)n
S=2
Predict the next term:
3,6,9,14,22,35,...
57
In an arithmetic sequence the 4th term is 17 and the common difference is d=3. What is the first term?
a4=a1+3d=17
a1+9=17
a1=8
In a geometric sequence, a1=5, and a4=135. What is the common ratio?
r=3
n=1
k=4
x=2k+1
24
Find the sum of the infinite series:
n=0
x=5/10n
S=50/9
Assume that the pattern continues, then create an equation for the nth term.
5,13,21,29
an=8n-3
Find Sn for the indicated arithmetic series:
S30 for the series with t1=17 and d=10
S30=3990
In a geometric sequence, a3=16, and r=2. Find the term a1.
a1=4
n=1
k=4
x=k2+2
38
Does this infinite series diverge or converge?
n=1
x=1/n2
Converges
Create an explicit equation for the sequence:
3,8,15,24,35,48,63
an=n2+2n
Find the number of terms in the partial sum:
Sn=3219
t1=15
d=4
37 terms
Find the sum if the first 6 terms of the geometric series where a1=2 and r=3.
S6=728
n=1
k=6
x=(-1)k+1 *k
-3
Find the sum of the infinite series:
n=0
x=(-1)n *(1/3)n
S=3/4
Create a recursive equation for the sequence:
2,5,12,29,70,169,408
a1=2, a2=5
an=2an-1+an-2 for n>2
The sum of the first 10 terms of an arithmetic sequence is 120, and the first term is 3. What is the common difference?
d=2
In a geometric sequence, the 2nd term is 12, and the 5th term is 96. What is the common ration and the first term
r=2
a1=6
n=3
k=5
x=log(k-1)k=100
x=72.453
Does this infinite series diverge or converge? Find the sum.
n=0
x=(-1)n *(3/4)n
Converges
S=4/7