Answer:
Adrian would make $196000 in his 26th year working.
Step-by-step explanation:
Adrian salary in first year = $66,000
As Adrian is expected to get raises of $5,000 every year going forward.
Here is the sequence of Adrian's raises:
5,000, 10000, 15000, 20000, 25000 .....
As the common difference between consecutive terms is constant.
d = 10000 - 5,000 = 5,000 ⇒ d = 15000 - 10000 = 5,000
So, Adrian's raises is in Arithmetic sequence.
a₁ = 5,000
n = 26
[tex]{\displaystyle \ a_{n}=a_{1}+(n-1)d}[/tex]
Put n = 26 to get the total amount of salary raises in Adrian's 26th year.
[tex]{\displaystyle \ a_{26}=5000+(26-1)5000}[/tex]
[tex]{\displaystyle \ a_{26}=5000+(25)5000}[/tex]
[tex]{\displaystyle \ a_{26}=5000+125000}[/tex]
[tex]{\displaystyle \ a_{26}=130000}[/tex]
Total raises amount after 26th year = $130000
Adding total raises after 26th year to the initial salary would let us figure out the total salary Adrian would make in his 26th year.
So,
Total Salary after 26th year = initial salary + total raises of 26 years
= 66000 + 130000
= $196000
So, Adrian would make $196000 in his 26th year working.
Keywords: arithmetic sequence, salary, raises, common difference
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