Lionel wrote an arithmetic sequence. The first five terms of the sequence are shown below.
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First, lets create a equation for our situation. Let 
be the months. We know four our problem that <span>Eliza started her savings account with $100, and each month she deposits $25 into her account. We can use that information to create a model as follows:
</span>
<span>
We want to find the average value of that function </span>from the 2nd month to the 10th month, so its average value in the interval [2,10]. Remember that the formula for finding the average of a function over an interval is:
. So lets replace the values in our formula to find the average of our function:
![\frac{25(10)+100-[25(2)+100]}{10-2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B25%2810%29%2B100-%5B25%282%29%2B100%5D%7D%7B10-2%7D%20)
We can conclude that <span>the average rate of change in Eliza's account from the 2nd month to the 10th month is $25.</span>
</span>
<span>
We want to find the average value of that function </span>from the 2nd month to the 10th month, so its average value in the interval [2,10]. Remember that the formula for finding the average of a function over an interval is:
We can conclude that <span>the average rate of change in Eliza's account from the 2nd month to the 10th month is $25.</span>