Answer:
3,172
Step-by-step 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: [tex]a_{n} = a_{1} + (n-1)V[/tex]
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).
[tex]a_{52} = 10 + (52-1) * 2 = 10 + 102 = 112[/tex]
Now that we know she'll save $112 on the 52nd week, let's calculate the total, using this formula:
[tex]S_{n} = \frac{(a_{1} + a_{n}) * n}{2}[/tex]
We know n (52), a1 (10) and an (112), so...
[tex]S_{52} = \frac{(10 + 112) * 52}{2} = \frac{122 * 52}{2} = 3,172[/tex]
At the end of the year, she will have saved $3,172
