Question

Find the sum of the geometric sum: 12+36+108+ ... + 78,732

Answer 1

354,288
118,092
39,360
1,062,876

Answer 2

@freckles

Answer 3

hi can you help me

Answer 4

sum of n terms = a1 * r^n - 1
------
r - 1

r = common ratio = 36/12 = 3, a1 = first term = 12

Answer 5

ok

Answer 6

now we need to find the value of n

the general form is a1 , a1*r , a*1r^2

Answer 7

ok

Answer 8

so the nth term = a1 r^(n-1)

Answer 9

you know i actually like you u actually show me hoe and not except me to do it

Answer 10

you actually show how to do it so for that I THANKS YOU

Answer 11

most poeple just say the formula crap

Answer 12

well let 78,732 = 12* r^(n-1)

we need to solve this for n

Answer 13

ok whats r

Answer 14

oh sorry r = 3

Answer 15

ok

Answer 16

then what do i do

Answer 17

Ok divide both sides by 12 gives
3^(n-1) = 6561

Answer 18

now you can find the value of n by taking logs of both sides
can you do that?

Answer 19

yes i got the A option

Answer 20

also just know that mathman said it was C

Answer 21

so what did you get dude

Answer 22

I dont think its either

taking logs

(n -1) ln 3 = ln 6561
n - 1 = ln6561 / ln 3 = 8
n = 9

Answer 23

so S9 = 12 * 3^9 - 1
------
3 - 1

Answer 24

can you work that out?

Answer 25

3^9 = 19683

so subtract 1 from that
then divide by 2
then multiply by 12 and you have the answer

Answer 26

yes one sec

Answer 27

you cant do that its a deciaml

Answer 28

??

Answer 29

u cant do that

Answer 30

u get a decimal

Answer 31

dude just tell me what you got

Answer 32

@freckles

Answer 33

i keep getting decimals

Answer 34

I can tell you the answer but I'd rather you work it out from the expression I gave you

its 12 * (3^9 - 1) / 2

just grab ur calculator and compute it

Answer 35

\[12 \cdot \frac{1-3^9}{1-3}\]
what did you get when you input into the calculator @Howard-Wolowitz ?

Answer 36

this one actually comes out to be a pretty whole number

Answer 37

let me do that

Answer 38

yes

Answer 39

i got -19685

Answer 40

no
are you doing the calculations in the right order/
first work out 3^9
then subtract 1 from the result
then divide by 2
finally multiply by 12

Answer 41

what kinda calculator are you using?
it is a ti-83 or one of those one entry type calculators ?

Answer 42

my phone

Answer 43

ewww
so it is most likely one entry
can your phone do exponents?

Answer 44

ok i did the frist step and got 19683

Answer 45

then the second step got me to 19682

Answer 46

so then you ahve this
\[12 \cdot \frac{1-19683}{1-3}\]

Answer 47

thats correct
now subtarct 1 from that

Answer 48

\[12 \cdot \frac{-19682}{1-3}\]

Answer 49

or you can do its freckles way

Answer 50

either way
it doesn't matter

Answer 51

the third i got a decimal

Answer 52

it will give the same result

Answer 53

wait how did you get a decimal ?

Answer 54

i cant do it that way freckles on my phone

Answer 55

1-3=?

Answer 56

-2

Answer 57

\[12 \cdot \frac{-19682}{-2} \\ 12 \cdot \frac{19682}{2}\]

Answer 58

so how did you get a decimal here ?

Answer 59

third is 9841 1/2

Answer 60

how did you get that

Answer 61

or 19683/2

Answer 62

\[12 \cdot \frac{19682}{2} \text{ is the same as } \frac{12}{2} \cdot 19682 \]
without using a calculator tell me what is 12/2 ?

Answer 63

- you dont find a third - you divide by 2
the 3 -1 on bottom is worked out first before you do the divide

Answer 64

ok so now just do that ok one sec

Answer 65

\[12 \cdot \frac{1-3^9}{1-3}=\frac{12}{1-3} \cdot (1-3^9)=\frac{12}{-2}(-19682) \\ =\frac{12}{2}(19682)=6(19682)=?\]

Answer 66

Ok I got B

Answer 67

118,092

Answer 68

is that right

Answer 69

ok
and you might want to practice on the actual calculator that you can use on a test

Answer 70

pretty sure most instructors don't let you use phones on test