OpenStudy (samsan9):

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.

3 years ago
OpenStudy (miracrown):

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

3 years ago
OpenStudy (samsan9):

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

3 years ago
OpenStudy (miracrown):

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

3 years ago
OpenStudy (miracrown):

yup, that's correct!

3 years ago
OpenStudy (samsan9):

365

3 years ago
OpenStudy (samsan9):

and 3 in a1 as well?

3 years ago
OpenStudy (miracrown):

Should look like this: \[S _{365} = \frac{ 365 }{ 2 } (3 + a _{365} ) \]

3 years ago
OpenStudy (miracrown):

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?

3 years ago
OpenStudy (samsan9):

a + d(n-1) i belive

3 years ago
OpenStudy (miracrown):

yup

3 years ago
OpenStudy (samsan9):

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

3 years ago
OpenStudy (samsan9):

its been a whole year since ive done these :/

3 years ago
OpenStudy (miracrown):

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3 years ago