A man worked for 10 years and received a raise of ₱5,000 at the beginning of each year after the first. If his salary was ₱14,320 the first year, find his salary the last year and the total amount received for the entire 10 years
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A man worked for 10 years and received a raise of ₱5,000 at the beginning of each year after the first. If his salary was ₱14,320 the first year, find his salary the last year and the total amount received for the entire 10 years
Since the salary is being increased by a fixed amount, we can model this as an arithmetic sequence with the first term (a) as the first salary (₱14,320) and the common difference (d) as the increase amount (₱5,000). The salary in the 10th year is the 10th term of the AP.
The nth term of an AP is given by
, thus 
.
Therefore, the salary in the last year is ₱59,320.
The total amount received for the entire ten years is the sum of the first 10 terms of the AP. The sum of the first n terms of an AP is given by
, where 
is the first term and 
is the last terms.
Thus the total salary received is
.