Question

PLEASE HELP RIGHT AWAY!!1

Answer 1

3,172

Explanation:

The "Money saved that week" is an arithmetic progression, where the next term is found by adding a constant value to the previous term. In this case, the variation is 2.

So that could be modeled with this equation:
`a_(n) = a_(1) + (n-1)V`

Where a1 is the first term of the series, in our case: 10, and the V is the variation each week, in our case: 2.

To be able to calculate the overall sum and answer the question, we first need to calculate the amount she will save on the last week (n=52).

`a_(52) = 10 + (52-1) * 2 = 10 + 102 = 112`

Now that we know she'll save $112 on the 52nd week, let's calculate the total, using this formula:

`S_(n) = ((a_(1) + a_(n)) * n)/(2)`

We know n (52), a1 (10) and an (112), so...

`S_(52) = ((10 + 112) * 52)/(2) = (122 * 52)/(2) = 3,172`

At the end of the year, she will have saved $3,172