WORKSHEET: Arithmetic Sequence & Series Word Problems
When solving word problems:
First, decide if you’re looking for a specific term in your sequence, or if you need to find the sum. It may also help to identify what’s given. Then use the formulas below to help!
The general term of an arithmetic sequence is given by the formula
an = a1 + (n - 1)d
Tips for Finding the sum of a given arithmetic sequence:
1. Identify a1, n, and an for the sequence.
2. If an, a1, or n is not given, Find it using an = a1 + (n - 1)d.
3. Substitute and evaluate: [pic]
1. Jerry deposited $20,000 on an investment that will add an additional $1,750 for every year that his money stays in the account. How much money will he have in his account at the end of year 8?
2. A theater has 32 rows of seats. If there are 26 seats in the 1st row, 30 in the 2nd, 34 in the 3rd, and so on, how many total seats are there in all?
3. In his piggy bank, Bingo dropped $1.00 on May 1, $1.75 on May 2, $2.50 on May 3 and so on until the last day of May.
a) How much did he drop in his piggy bank on May 19?
b) What was his total deposit in his piggy bank for the month of May?
1. You borrow money for a new car from the bank. After month 1, the loan balance is $14,760. After month 2, it is $14,520. If this pattern continues, what will the balance be after 21 years?
2. A theater has 56 rows of seats. If there are 13 seats in the 1st row, 17 in the 2nd, 21 in the 3rd, and so on, how many total seats are there in all?
3. Jerry deposited $950 on an investment that will add an additional $80 for every year that his money stays in the account. How much money will he have in his account at the end of year 9? *Be careful! $950 is the initial amount, not the first term!
4. A tube well is bored 800 meters deep. The 1st meter costs $250 and the cost per meter increases by $50 for every subsequent meter. Find the cost of boring the 750th meter.
5. There are 20 rows of seats on a concert hall: 25 seats are in the 1st row, 27 seats on the 2nd row, 29 seats on the 3rd row, and so on. If the price per ticket is $300, how much will be the total sales for a one-night concert if all seats are taken?
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