1. Find the 7^th term, if the first term is 3, and the second term is 5.
    
2. Find the 3^rd term, if the first term is 9, and the common difference is – 2.
    
3. Find the 1^st term, if the third term is 12, and the second term is 8.
    
4. Find the 10^th term, if the fifth term is 0, and the seventh term is 5.
    
5. Find the first term, if the sum of the second and third terms is 51, and the common difference is 5.
    
6. Find the first term if the second term is
   11

   2
    and the fourth term is 9.
    
7. If the sum of the first three terms of an arithmetic sequence is 102, find the second term.
    
8. The sum of the n^th term and the (n + 1)^th term is 62. The sum of the first and second terms is 14. The sum of the third and fourth terms is 22. Find n.
    
9. The common difference is two more than the first term. The fourth term is 30. What is the first term?
    
10. The sum of the squares of the first two terms is 52. The common difference is 2. What are the possible values for the first term?
     
11. In 2010, the population of Gooberville was 3,200. The population increases by 120 every year. What will the population be in 2025?
     
12. The price of a widget increases by $0.03 every year. If its current price is $17.20, what was the price 15 years ago?

For each problem below, the sequence is geometric

1. Find the third term if the first term is 10 and the second term is 15.
    
2. Find the first term if the fifth term is 128 and the common ratio is 2.
    
3. Find the fifth term if the second term is 9 and the third term is -3.
    
4. The common ratio is equal to the first term, and the sum of the first two terms is 2. Find all possible values for the first term.
    
5. If the fifth term is 81 and the seventh term is 9, what are all possible values for the sixth term?
    
6. The second term is three more than the first term, and the fourth term is four more than the third term. What is the common ratio?
    
7. The fourth term is 18 more than the opposite of the third term, and the second term is 24. What are the possible values for the common ratio?
    
8. The population of City A doubles every year. Its current population is 102,400. What was its population ten years ago?
    
9. Every year Jethro’s taxes increase by 5%. This year his taxes were $2,000. What will his taxes be 20 years from now? Give your answer to the nearest dollar.

For each problem below, the series is arithmetic.

1. If the first term is 3, and the common difference is 9, what is the sum of the first 20 terms?
    
2. If the second term is 10 and the third term is 15, what is the sum of the first 10 terms?
    
3. If the sixth term is 12 and the tenth term is 4, what is the sum of the first 10 terms?
    
4. The sum of the first 9 terms of an arithmetic series is 0. The common difference is -2. What is the first term?
    
5. The sum of the first 6 terms of an arithmetic series is 84. The sixth term is 19. What is the first term?
    
6. Each year I earn $1,010 more than I did the previous year. If I earned $25,000 this year, what will be my total earnings for the next ten years?

1. What is the sum of the first 5 terms of the series 1 +
   1

   2
   +
   1

   4
   + ...?
    
2. What is the sum of the first 6 terms, if the first term is 8 and the second term is 12?
    
3. What is the sum of the first 4 terms, if the sum of the first two terms is 12, and the common ratio is
   1

   2
   ?
    
4. What is the sum of the first 6 terms of the series 8 - 4 + 2 - ...?
    
5. Today Toby ate one piece of candy. Tomorrow he’ll eat two pieces of candy. The next day he’ll eat four pieces of candy. Each day he doubles the amount of candy he eats. How many pieces of candy will he eat in twenty days?
    
6. Find the sum of the series with first term 7, and common ratio
   1

   2
   .
    
7. Find the sum of the series with first term 1 and common ratio
   2

   3
   .
    
8. Find the sum of the series with first term 2 and common ratio -
   1

   3
   .
    
9. The sum of the series is 10, and the common ratio is
   1

   5
   . What is the first term?
    
10. The sum of the series is 4, and the first term is 1. What is the common ratio?
     
11. The common ratio of a series is a third of the first term. The sum is
    9

    2
    . What is the first term?