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

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

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.

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.

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

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.

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.

To find the 29th term of the sequence 21, 15, 9, 3, . . ., we need to determine the pattern. This appears to be a decreasing arithmetic sequence with a common difference of -6.

To find the nth term of an arithmetic sequence, we use the formula:

tn = a + (n - 1)d

Where:
tn is the nth term
a is the first term
n is the position of the term
d is the common difference

Plugging in the values from the given sequence, we have:

t29 = 21 + (29 - 1)(-6)

Simplifying further:

t29 = 21 + 28(-6)
t29 = 21 - 168
t29 = -147

So, the 29th term of the sequence is -147. Therefore, the correct answer is option A) –147.

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To evaluate the series 1 + 0.1 + 0.01 + ..., we notice that each term is obtained by dividing the previous term by 10. This is a geometric series with a common ratio of 1/10.

The sum of an infinite geometric series can be calculated using the formula:

S = a / (1 - r)

Where:
S is the sum of the series
a is the first term
r is the common ratio

Plugging in the values from the given series, we have:

S = 1 / (1 - 1/10)

Simplifying further:

S = 1 / (9/10)
S = 10/9

So, the sum of the series is 10/9. Therefore, the correct answer is option A) 1.11.