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Claire saves one month and then each month thereafter she saves more than the preceding month for a -year period
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Q. Claire saves one month and then each month thereafter she saves more than the preceding month for a -year period
- Calculate First Month Savings: Determine the amount saved in the first month.Claire saves in the first month.
- Calculate Monthly Increase: Determine the monthly increase in savings. Claire saves more than the preceding month for each subsequent month.
- Calculate Total Months in Years: Calculate the total number of months in a -year period.There are months in a year, so in years, there are months. months.
- Recognize Arithmetic Sequence Pattern: Recognize the pattern of savings as an arithmetic sequence. The amount saved each month forms an arithmetic sequence where the first term is \$\(45\)\ and the common difference is \$\(4\).
- Calculate Last Term of Sequence: Calculate the last term of the arithmetic sequence.\(\newline\)The last term \(l\) can be calculated using the formula \(l = a + (n - 1)d\), where \(a\) is the first term, \(n\) is the number of terms, and \(d\) is the common difference.\(\newline\)\(l = 45 + (192 - 1)\times 4\)\(\newline\)\(l = 45 + 191\times 4\)\(\newline\)\(l = 45 + 764\)\(\newline\)\(l = 809\)
- Calculate Sum of Sequence: Calculate the sum of the arithmetic sequence.\(\newline\)The sum \(S\) of an arithmetic sequence can be calculated using the formula \(S = \frac{n}{2} \times (a + l)\), where \(n\) is the number of terms, \(a\) is the first term, and \(l\) is the last term.\(\newline\)\(S = \frac{192}{2} \times (45 + 809)\)\(\newline\)\(S = 96 \times 854\)\(\newline\)\(S = 81984\)
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