# First Six Terms

Pro Problems > Math > Algebra > Functions > Arithmetic Sequences > Series## First Six Terms

The sum of the first 6 terms of an arithmetic series is 84. The sixth term is 19. What is the first term?

## Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.## Similar Problems

### Tower of Blocks

150 blocks are stacked to make a tower. Each tier of the tower must have at least three more blocks than the tier above it. If the tower is made as tall as possible, with the fewest number of blocks, how many blocks will be left over?

### All the King's Horses

On the first day of his reign, which was a Monday, King Midas received 5 horses. On each successive day, he received 1 more horse than he received the previous day. After a week, he began turning horses to gold. First he turned 20 horses to gold, and then on each successive Monday, after receiving his daily horses, he turned 60 more horses to gold than he did the previous Monday.

How long will it take before all of the king's horses have been turned to gold?

### Job's Trials

On the first day, one of Job's sheep died. On each day after that, one more sheep died than on the previous day.

On the second day, one of Job's cows died. On each day after that, two more cows died than on the previous day.

On the third day, one of Job's goats died. On each day after that, three more goats died than on the previous day.

If sheep a sheep costs $400, a cow costs $1200, and a goat costs $600, how much money had Job lost after 7 days?

### Howard's Salary

Howard's salary increases by $1,500 every year. If he works for 25 years, he earns $1,262,500.

What was his original salary?

### Zero Sum

The sum of the first 9 terms of an arithmetic series is 0. The common difference is -2. What is the first term?

### Overdue Library Books

Toby took out more than one, but fewer than ten books from the library on the same day, and they were all overdue by less than a week when he returned them all on the same day. The library charges a certain amount (which is less than a quarter) for the first day a book is overdue, and then on each successive day, an additional fee is applied, which is one cent more than the previous day's fine. Toby's fine for his library books was $4.75.

How much is the fine for the first day for one library book overdue?

# Ask Professor Puzzler

Do you have a question you would like to ask Professor Puzzler? Click here to ask your question!**Get a**

*FREE*Pro-Membership!Educators can get a free membership simply by sharing an original lesson plan on our

*Articles for Educators*page!