Question

Find the sum of the first 25 terms of a geometric sequence where the first term is 177,147 and the common ratio is -1/3

Answer 1

A. 132,860.1667
B. 132,860.25

Answer 2

C. 132,860

Answer 3

D. 132,860.5

Answer 4

@freckles

Answer 5

@Michele_Laino

Answer 6

HEy freckls!

Answer 7

MY TWO FRIENDS!!

Answer 8

\[a_1=177,147 \\ r=\frac{-1}{3} \text{ and you want to add all the way up the n=25th term }\\ \sum_{i=1}^{n}a_i=a \cdot \frac{1-r^n}{1-r}\]
all this info is given
just plug in

Answer 9

a is a_1 by the way

Answer 10

please try this formula:
\[{S_n} = {a_1}\frac{{1 - {q^n}}}{{1 - q}}\]

Answer 11

Alright so I did that and got either C or B

Answer 12

where n= 25 and q=r =-1/3

Answer 13

ok so use that to do what subsuite

Answer 14

you can use a calculator right?

Answer 15

no

Answer 16

can you though

Answer 17

hint:
here is your substitution:
\[{S_n} = 177147\frac{{1 - {{\left( { - 1/3} \right)}^{25}}}}{{1 - \left( { - 1/3} \right)}}\]

Answer 18

what?
so you are really expected to do 3^(25) in your head?

Answer 19

Or on paper.

Answer 20

alright I'll use one

Answer 21

ok so you are going to input:
177147 times (1-(-1/3)^(25))/(1-(-1/3))

Answer 22

i got 847288609443

Answer 23

i did what you said

Answer 24

try it again
I don't think 177147 times (1-(-1/3)^(25))/(1-(-1/3))
equals that

Answer 25

3^25 is though

Answer 26

ok i didn't ask you to do that
i was just kinda like wow your teach expects you to do that without calculator

Answer 27

oh ok sorry my bad

Answer 28

please use Windows calculator @Howard-Wolowitz

Answer 29

ok im doing it one sec

Answer 30

dang i got a big number

Answer 31

−125099989649180177147

Answer 32

-125099989649180/177147

Answer 33

177,147*(1-(-1/3)^(25))/(1-(-1/3))
hmmm I don;t you input this because somehow you put 177147 on bottom

Answer 34

http://www.wolframalpha.com/input/?i=177%2C147*%281-%28-1%2F3%29%5E%2825%29%29%2F%281-%28-1%2F3%29%29

Answer 35

so off of that site im going with C

Answer 36

I think another choice is closer

Answer 37

I got a different option

Answer 38

do i use one of the .25 options from the site

Answer 39

that choice seems to be a lot closer

Answer 40

closer?

Answer 41

nearer to the value on that page I sent you

Answer 42

it said something like 132860.2500001568

Answer 43

132860 is close
but
132860.25 is a lot closer

Answer 44

using Windows calc I got this value:
132860,24999984319363140342327119

Answer 45

and @Michele_Laino value he got is still closer to 132860.25 than it is to 132860

Answer 46

ok so i got what he got then?

Answer 47

which is what?

Answer 48

.25

Answer 49

that's right!

Answer 50

well you mean the 132860.25 and yes that is what i got above

Answer 51

well i thought u meant i was close not right

Answer 52

no I was saying out of all the choices 132860.25 is the closest

Answer 53

please I think that you have to round off your result @Howard-Wolowitz

Answer 54

i gotcha

Answer 55

ok i got it

Answer 56

.5

Answer 57

is .5 right

Answer 58

@freckles