Suppose your salary is 45,000 and you receive a 1500 raise...

Suppose your salary is $\$ 45,000$ and you receive a $\$ 1500$ raise for each year you work for 35 years.
a. How much will you earn during the 35 th year?
b. What is the total amount you earned over your 35 -year career?

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Key Concepts

Arithmetic Series

An arithmetic series is the sum of the terms in an arithmetic sequence. It is applied to find the cumulative total over several periods, such as calculating the total earnings over multiple years by summing the annual salaries.

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This concept is used to calculate a specific term within a series, such as determining the salary in a particular year when annual increases are fixed.

Transcript

00:01 Your salary is $45 ,000.

00:02 You're going to receive a $1 ,500 raise each year, and you're going to work for a total of 35 years.

00:08 So in part a of this problem, we want to know how much money, or sorry, how much will you earn during the 35th year? well, in this case, this can be re -expressed using arithmetic sequence, because we have a starting value, 45 ,000, so that would be our a -1 value.

00:24 And because our raise is going to go up, or our salary is going up by $1 ,000 every year, that's our d value.

00:32 And because this is going to happen 35 times, we're essentially looking for the 35th term in this sequence.

00:38 So that means n would equal to 35.

00:40 So now we can go ahead and find what we'd be making after the 35th year.

00:45 Essentially, we need to find a sub n.

00:47 So we'll use our a sub n formula.

00:49 A subn is equal to a sub 1 plus d times m minus 1.

00:53 And now we'll substitute in our values.

00:56 So we'll have 45 ,000 plus d, which is 1500, times 35 minus 1.

01:03 So now you can go right to your calculator and you'll have 45 ,000 plus 1 ,500 times 35 minus 1 or simply just 34.

01:12 And you'll find that a sub n will equal to 96 ,000.

01:16 So that means after 36 years, or sorry, after 35 years that you'll be making $96 ,000 a year...

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