Question

If you save three pennies on January 1, six pennies on January 2, nine pennies on January 3, and continue this pattern for one year (not a leap year), what will be the value of your entire savings, in dollars, at the end of that one year? Express your answer as a decimal.

***Please show steps and explain!! :)

Answer 1

it sounds like the pattern is the 3s times table:

3,6,9,12,15,...

Answer 2

but we have to add that amount to the previous balance

Answer 3

it develops into a recursive equation

b1 = 3
b2 = 3 + 6 = 9
b3 = 3 + 6 + 9 = 18
b4 = 3 + 6 + 9 + 12 = 40

bn = b{n-1} + 3(n-1) maybe

Answer 4

from my memory banks; i think this might end up with some exponential closed form

Answer 5

\[\sum_{n=1}^{365}3n\]
perhaps is another way to notate it

Answer 6

i have no idea how to solve this :( so the equation we would use would be An=3+3(n-1) ??

Answer 7

we can test out the 3+3(n-1) and see how it might play out

when n=1; a=3
when n=2; a=6
when n=3; a=9

that works for the amount of money you put in each time, but it doesnt keep track of the balance that accumulates

Answer 8

Oooops! I meant this:
\[\large \sum_{k=1}^nk = \frac{n(n+1)}{2}\]

Answer 9

wait so do i use wio's equation to solve?? i'm confused... :O cuz i need to use an equation right?? otherwise that would take forever to plug in numbers and stuff??

Answer 10

if u find sum of the series 3+3(n-1) till 365 terms.....u can get it.....maybe..

Answer 11

wios formula is for the sum of an arithmetic series with "k" terms

im not sure if its the proper setup for you problem tho; but it does play a part

Answer 12

ohhh okat so what equation do i use then?

Answer 13

3(1) + 3(2) + 3(3) + ... + 3(365)

3(1+2+3+ ... +365)

Answer 14

okay, following :)

Answer 15

\[3\frac{1+365}{2}\]should do it

Answer 16

3*n(n+1)/2
n=365

Answer 17

could i use this equation?? Sn=(n/2)[2a+(n-1)d]

Answer 18

yes, same answer u will get

Answer 19

oh so n=365 represents number of terms??

Answer 20

... i forgot the extra "n" in the latex :/

Answer 21

You mean \[\Large 3 \cdot \frac{365(365+1)}{2}\]

Answer 22

correct wio ;)

Answer 23

yup, n= no. of terms = 365 here
and if this question belongs to topic series, the u use that sn formula only....

Answer 24

So if i plug into your equation who, then i get 200385
and if i plug into my equation, i get this:
n= 365 terms
a=1st term which = 3
d= common difference b/w each terms which is 3

Sn=(365/2)[2*3+(365-1)3]
=(365/2)[6+(364)3]
=(365/2)[6+1092]
=(365/2)(1098)
=365*549
=200385
????

Answer 25

is that right??? cuz i got the same thing twice???

Answer 26

yup, even i got that

Answer 27

lol, with any luck when you get the same thing twice its correct; but theres always the possibility that you might of just done 2 things incorrectly

Answer 28

these are pennies, u need to convert them in dollars

Answer 29

and so the simplest way to show the work would probably be