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.

Answer 1

This is a sequence type problem
3,6,9,12,---
and there are 365 days in a year
so that's what n, the number of terms, is

n= 365

this is an arithmetic sequence, so they're asking us to add up the money
the formula for the sum of a finite arithmetic sequence is:

\[S _{n}= \frac{ n }{ 2 } (a _{1}+ a _{n} )\]

Answer 2

so do I plug in 365 into the n in this formula and 3

Answer 3

So looking at the formula above^ , what is n?

Answer 4

yup, that's correct!

Answer 5

365

Answer 6

and 3 in a1 as well?

Answer 7

Should look like this:

\[S _{365} = \frac{ 365 }{ 2 } (3 + a _{365} ) \]

Answer 8

so our stuff is plugged in ^
however, to finish up the problem, we need to know what a365 is
Is there a formula for a specific term of an arithmetic sequence?

Answer 9

a + d(n-1) i belive

Answer 10

yup

Answer 11

so we just plug in the same numbers into this formula i am assuming

Answer 12

its been a whole year since ive done these :/