1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4

A)15
B)15/2
C)-15
D)1/15
I chose A

2)Find the sum of the infinite geometric series. Sigma sign with infinity symbol above and n=1 below. To the right 20(-1/4)n-1
A)25
B)80/3
C16
D)does not exist
I chose A

3)Find the sum of the infinite geometric series:4+3+9/4+:...
A)16/7
B)16
C)-12
D)does not exist
I chose B

4)Write 0.72 repeating as a fraction.
A)7/9
B)8/11
C)18/25
D)7 and 2/9
I chose B but my book confuses me on how to work it out. I just divided 8 and 11 and I got .72 repeating

5)Find the fifth term of the sequence in which a1=-3,and aN+1=3aN-n
A)-301
B)-99
C)-193
D)-341
I don't know

1. I chose B

2. C
3. Hey, I better start showing you how

1. Plain geometric series
Sn = g(1-r^n)/(1-r)

300 = g (1-3^4) /1-3

300 = g (1-81) / -2

g = 300 (-2/-80)

g = 15/2

2. sigma = g/(1-r)
g=20
r=-1/4
sigma = 20/1.25
= 2000/125
= 400/25
= 16

3. g = 4
r = 3/4
s = 4/(1-3/4)
=16

4. .72 72 72 72 ....
= 72 10^-2 + 72 10^-2 10^-2 +72 (10^-2)^3 ...

this is geometric series with
g = 72*10^-2
r = 10^-2
so

s = 72*10^-2/(1-.01)
= .72/.99
= 8/11

I do not understand the last one.

thanks for the help. are you possitive they are correct?

Oh good heavens, always check anything I do!

1) To find the first term (a1) in a geometric series given the sum (Sn), common ratio (r), and number of terms (n), you can use the formula: Sn = a1 * (1 - r^n) / (1 - r)

In this case, Sn = 300, r = -3, and n = 4
Substituting these values into the formula: 300 = a1 * (1 - (-3)^4) / (1 - (-3))

Simplifying: 300 = a1 * (1 - 81) / (1 + 3)
300 = a1 * (-80) / 4
300 = -20 * a1

Dividing both sides by -20, we get: a1 = -300 / 20 = -15

Therefore, the answer is C) -15.

2) To find the sum of an infinite geometric series, you can use the formula: S = a1 / (1 - r)

In this case, a1 = 20 and r = -1/4
Substituting these values into the formula: S = 20 / (1 - (-1/4))
Simplifying: S = 20 / (1 + 1/4) = 20 / (5/4)

To divide by a fraction, you multiply by its reciprocal: S = 20 * (4/5) = 16

Therefore, the answer is C) 16.

3) To find the sum of an infinite geometric series, you can use the formula: S = a1 / (1 - r)

In this case, a1 = 4 and r = 3/4
Substituting these values into the formula: S = 4 / (1 - 3/4)

To divide by a fraction, you multiply by its reciprocal: S = 4 * (4/1) / (1/4) = 16

Therefore, the answer is B) 16.

4) To convert a repeating decimal (0.72 repeating) into a fraction, you can use the following steps:

Let x = 0.7272...

Multiply both sides of the equation by 100 to remove the decimal point: 100x = 72.7272...

Subtract the original equation from the above equation to eliminate the repeating part:
100x - x = 72.7272... - 0.7272...

Simplifying the equation: 99x = 72

To solve for x, divide both sides of the equation by 99: x = 72 / 99 = 8/11

Therefore, the answer is B) 8/11.

5) To find the fifth term of a sequence defined by the relationship a1 = -3 and aN+1 = 3aN - N, you can use the recursive formula to generate the sequence:

a1 = -3
a2 = 3*(-3) - 1 = -10
a3 = 3*(-10) - 2 = -32
a4 = 3*(-32) - 3 = -99

Therefore, the answer is B) -99.