Question

Salary. Suppose your salary is 45,000 dollars and you receive a 1500 dollars 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?

Name: Problem 68, Chapter 10: Precalculus
Uploaded: 2020-06-13T00:12:53-08:00
Duration: 1 min 27 s
Channel: Amy Jiang
Description: Salary. Suppose your salary is 45,000 dollars and you receive a 1500 dollars 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?

   Salary. Suppose your salary is 45,000 dollars and you receive a 1500 dollars 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?

Precalculus

Cynthia Young 2nd Edition

Chapter 10, Problem 68

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Solved by Expert Amy Jiang

06/13/2020

Step 1

This is an arithmetic sequence where the first term (a) is 45,000 dollars, the common difference (d) is 1500 dollars, and the number of terms (n) is 35. The nth term of an arithmetic sequence can be calculated using the formula: $$ a_n = a + (n-1)d $$ Substituting Show more…

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Salary. Suppose your salary is 45,000 dollars and you receive a 1500 dollars 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 represents the sum of the terms of an arithmetic sequence. In this context, calculating the total salary earned over 35 years involves summing up the salaries of each year, which can be efficiently done using the arithmetic series sum formula (S? = n/2(a? + a?)).

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This concept is essential here because the yearly salary increase follows a fixed amount each year, making the salary progression an arithmetic sequence.

Nth Term of an Arithmetic Sequence

The nth term formula (a? = a? + (n-1)d) is used to calculate the salary in any given year based on the starting salary and the constant raise. It allows you to determine the salary in the 35th year by counting the number of increments from the initial salary.

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