Certainly! Let's go through the process of determining your savings over 10 weeks.
Let's assume you decided to save a fixed amount each week, starting with [tex]$1 in the first week. We can represent your savings over 10 weeks as an arithmetic sequence.
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. In this case, our weekly savings increase by the same amount every week.
For the first week, you save $[/tex]1.
For the second week, you save [tex]$2.
For the third week, you save $[/tex]3.
And this pattern continues.
To find the total savings for each week, we can set up the sequence as follows:
1st week: [tex]$1
2nd week: $[/tex]2
3rd week: [tex]$3
4th week: $[/tex]4
5th week: [tex]$5
6th week: $[/tex]6
7th week: [tex]$7
8th week: $[/tex]8
9th week: [tex]$9
10th week: $[/tex]10
Therefore, the arithmetic sequence representing your savings over 10 weeks is:
[tex]\[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \][/tex]
This sequence shows the amount saved in each week: starting from [tex]$1 in the first week and increasing by $[/tex]1 each subsequent week until the 10th week.
