Evaluate the series 72 + 12 + 2 + ...
A) 14.4
B) 432
C) 6
D) 86.4***
When it says evaluate that means add the series together, right? When I add them together I get 86 which isn't an answer, or does it mean common ratio which is 6 which is an answer.
Find the 29th term of the following sequence.
21, 15, 9, 3, . . .
A) –147
B) –165
C) –153***
D) –159
Evaluate the series 1 + 0.1 + 0.01 + ...
A) 1.11***
B) 1.12
C) 0.33
D) 2
6 answers
21, 15, 9, 3, . . .
15 - 21 = - 6
9 - 15 = - 6
3 - 9 = - 6
This is an arithmetic sequences.
First term a1 = 21
Common difference: d = - 6
nth term of the arithmetic sequence:
an = a1 + ( n - 1 ) ∙ d
In this case n = 29
a29 = 21 + ( 29 - 1 ) ∙ ( - 6 )
a29 = 21 + 28 ∙ ( - 6 )
a29 = 21 - 168
a29 = - 147
15 - 21 = - 6
9 - 15 = - 6
3 - 9 = - 6
This is an arithmetic sequences.
First term a1 = 21
Common difference: d = - 6
nth term of the arithmetic sequence:
an = a1 + ( n - 1 ) ∙ d
In this case n = 29
a29 = 21 + ( 29 - 1 ) ∙ ( - 6 )
a29 = 21 + 28 ∙ ( - 6 )
a29 = 21 - 168
a29 = - 147
I thought I was doing something wrong with the first one. Good thing I doubled checked. The second and third ones are confusing me though. They both say evaluate.
The second has the sum but not the common ratio and the third has the common ratio but not the sum.
The second has the sum but not the common ratio and the third has the common ratio but not the sum.
72, 12 , 2..
geometric sequence.
first term a = 72
common ratio r = 1 / 6
∑ 0 to infinity = a / ( 1 - r ) =
72 / ( 1 - 1 / 6 ) =
72 / ( 6 / 6 - 1 / 6 ) =
72 / ( 5 / 6 ) = 72 * 6 / 5 = 432 / 5 = 86.4
geometric sequence.
first term a = 72
common ratio r = 1 / 6
∑ 0 to infinity = a / ( 1 - r ) =
72 / ( 1 - 1 / 6 ) =
72 / ( 6 / 6 - 1 / 6 ) =
72 / ( 5 / 6 ) = 72 * 6 / 5 = 432 / 5 = 86.4
I am starting to understand this a little better.
I am going to try to do the second question. I will post it on here after I do it so you can see if I am doing it correctly.
I am going to try to do the second question. I will post it on here after I do it so you can see if I am doing it correctly.
1, 0.1, 0.01
first term a = 1
common ratio r = 1/10
Sigma 0 to infinity = 1/(1-1/10)
1/(10/10-1/10)
1/(9/10) = 1*10/9=1.11...
Do I divide by 9 at the end since you divided by 5 at the end? How would you know when to divide.
first term a = 1
common ratio r = 1/10
Sigma 0 to infinity = 1/(1-1/10)
1/(10/10-1/10)
1/(9/10) = 1*10/9=1.11...
Do I divide by 9 at the end since you divided by 5 at the end? How would you know when to divide.