Question

What are the first five partial sums of the geometric series: an = (5/8)*3^n-1?show work

Student Answer: A. 0.625, 1.875, 5.625, 16.875, 50.625
B.1.875, 3.75, 7.5, 13.1250, 20.625
C. 2.5, 4.375, 10, 26.875, 77.5
d. 0.625, 2.5, 8.125, 25, 75.625

Answer 1

Let's start by calculating n = 0.

Answer 2

okay

Answer 3

is it a 11

Answer 4

Wait... can you rewrite the problem with the equation tool?

Answer 5

Just a_n

Answer 6

\[a_n = \frac{ 5 }{ 8 }*3^n-1\] or\[a_n = \frac{ 5 }{ 8 }*3^{n-1}\]

Answer 7

an(5/8)*3^n-1

Answer 8

its the second one

Answer 9

is it d

Answer 10

but i need to show work ugh math

Answer 11

Since it's the second one, we start with an index of 1. What is n = 1? Sorry for the lag in response.

Answer 12

D is correct by the way. Let me know if you want an explanation.

Answer 13

he told me i need to show my work
can u help me plz

Answer 14

Yes. Let's find the first partial sum. What is the sum when n = 1?

Answer 15

um 4

Answer 16

idk i am confused

Answer 17

How did you get four? When n = 1, \[a_1 = (5/8)*3^0 = (5/8)*1 = 5/8\]

Answer 18

oh my bad i wrote it wrong

Answer 19

As in the series is written incorrectly?

Answer 20

i put (5/8)*1+3 but i re written it

Answer 21

Ok, so you understand how we got a_1 then?

Answer 22

yeah

Answer 23

OK, this is our first partial sum. Now what is a_n when n =2? Adding a_1 and a_2 together will give you your second sum.

Answer 24

okay

Answer 25

What did you get?

Answer 26

so u add n-1+n-2

Answer 27

No, my apologies for the confusing type. I mean,\[a_1 = 5/8\]\[a_2 = (5/8)*3^{1}\]
Adding these together yields your second partial sum.

Answer 28

Does that make sense?

Answer 29

some what sorry i am bad at math

Answer 30

i give up

Answer 31

\[\sum_{n = 1}^{5}\frac{ 5 }{ 8 }3^{n-1} = \frac{ 5 }{ 8 }3^0 + \frac{ 5 }{ 8 }3^1 +\frac{ 5 }{ 8 }3^2 +...+\frac{ 5 }{ 8 }3^5 = \frac{ 5 }{ 8 }(1 + 3 + 9 + 27 + 81)\]
\[\sum_{n = 1}^{1}\frac{ 5 }{ 8 }3^{n-1} = \frac{ 5 }{ 8 }3^0\]
\[\sum_{n = 1}^{2}\frac{ 5 }{ 8 }3^{n-1} = \frac{ 5 }{ 8 }3^0 + \frac{ 5 }{ 8 }3^1\]
. . .

Answer 32

then u divide right

Answer 33

Divide? What would you divide by?

Answer 34

ugh idk this is hard

Answer 35

I'm sorry that I cannot help you better.

Answer 36

It's really quite simple. Maybe try again later?

Answer 37

i dont know what to do on this is hard for me lol