Jacie is considering a job that offers a monthly starting salary of $3000 and guarantees her a monthly raise of
$180 during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at
the end of her first year/
3000, 3180, 3360, 3540, 3720, ...
nth term= 3000+(180)(n)
n=0,1,2,3,4,5
Well, it looks like Jacie has landed herself a job! Let's calculate her monthly salary at the end of her first year.
To find the general term of an arithmetic sequence, we need to know the first term and the common difference. In this case, the first term is $3000, and the common difference is $180.
The general term (Tn) of an arithmetic sequence can be found using the formula:
Tn = a + (n - 1)d
Here, a represents the first term, n represents the term number, and d represents the common difference.
So, to find the monthly salary at the end of the first year (12 months), we substitute the values into the formula:
T12 = $3000 + (12 - 1) * $180
Simplifying the equation:
T12 = $3000 + (11) * $180
T12 = $3000 + $1980
T12 = $4980
Therefore, Jacie's monthly salary at the end of her first year would be $4980.
Hope that puts a smile on Jacie's face!
To find the general term of an arithmetic sequence, we need to identify the first term (a) and the common difference (d).
In this case, Jacie's starting salary is $3000, so the first term (a) is 3000. Additionally, she receives a monthly raise of $180, which means the common difference (d) is 180.
The formula for the general term of an arithmetic sequence is:
An = a + (n-1) * d
Here, n represents the position of the term in the sequence that we're looking for.
To find Jacie's monthly salary at the end of her first year, we need to calculate the term where n = 12 (since there are 12 months in a year).
Substituting the values into the formula, we get:
A12 = 3000 + (12-1) * 180
A12 = 3000 + 11 * 180
A12 = 3000 + 1980
A12 = 4980
Therefore, the general term of this arithmetic sequence is An = 3000 + (n-1) * 180, and Jacie's monthly salary at the end of her first year would be $4980.