Arithmetic
Sequence
Sequence
What is the common difference in the sequence?
-7, -5, -3, ...
2
What is the first term in the series?
3
a1= 5(1)-2= 3
What is the common ratio in the sequence?
3, 9, 27, ...
3
r = 9/3 = 3
What is the first term in the series?
6
Which of the following is an arithmetic sequence?
a. 12, -12, -12, -12, ...
b. 32, 8, 2, 1/2, ...
c. 1, 2, 3, 5, 8, ...
d. 5, 8, 11, 14, ...
d. 5, 8, 11, 14, ...
What is the common difference in the series?
5
d = 8 - 3 = 5
What is the common ratio in the sequence?
27, 3, 1/3, 1/27, ...
r = 3/27 = 1/9
What is the common ratio in the series?
2
What is the nth term in the sequence?
1, 5, 9, 13, ....
an = a1 + (n-1) d
an = 1 + (n-1) (4) = 1 + 4n -4
an =4n - 3
What is the partial sum of the series?
126
Sn= n/2 (a1+an) = 7/2 (3+33) = 7/2(36) = 7(18) = 126
Which of the following is an arithmetic sequence?
a. 12, 8, 4, 0, -4, ...
b. 6, 12, 6, 12, 6,...
c. 1/4, 1/2, 1, 2, 4,...
d. 2, 4, 6, 8, 10, 12, ...
c. 1/4, 1/2, 1, 2, 4, ...
What is the last term of the series?
96
Fill in the gaps of this arithmetic sequence.
-3, 2 , ___ , ___ , 17
7, 12
Given 125, 150, 175 , . . .
What is the sum of the first seven terms?
1400
Sn= 7/2 [2(125) +(7-1)(25) ] = 1400
What is the 5th term of the sequence?
1, −5, 25, ...
625
r = -5
a5= 1(5)4 = 625
What is the sum of the series?
186
What is the 12th term of the sequence?
34, 31, 28, 25, 22, ....
a12=1
a12= a1+(n-1)(d)
a12= 34 + (12-1)(-3) = 34 + (-33) = 1
Find the sum of the following series:
5, 9, 13, …, 101
1,325
101 = 5 + (n-1)(4)
n= 25
Sn= 25/2 [2(5)+(25-1)(4)] = 25/2 (106)
Sn= 25(53)=1,325
Fill in the gaps of this geometric sequence.
1, ___ , ___ , 1/8 , 1/16
1/2, 1/4
r = 1/2
What is the sum of the infinite geometric series?
1/2, 1/6, 1/18, 1/54, ...
3/4
Sn=a1/(1-r) = 1/2 /(1-1/3) = 3/4