# Seven Books

Pro Problems > Math > Algebra > Functions > Arithmetic Sequences## Seven Books

Geraldine has 7 books which she has placed in order from least number of pages to most. She notices that her books’ page counts are in arithmetic sequence. She further notices that the number of words per page decreases arithmetically from one book to the next. If the first book has 96,000 words, the last book has 123,132 words, and the middle book has 111,843 pages. Find the common difference in the sequence of the number of pages.

## 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

### N and N + 1

The sum of the n^{th} term and the (n + 1)^{th} term of an arithmetic sequence is 62. The sum of the first and second terms is 14. The sum of the third and fourth terms is 22. Find n.

### Odds and Evens

If you add the first five even numbered terms of an arithmetic sequence, the result is 27 more than if we had added the first five odd numbered terms. What is the common difference of the sequence?

### Common Difference Problem

The common difference in an arithmetic sequence is two more than the first term. The fourth term is 30. What is the first term?

### Sequence by Threes

The sum of the first three terms of an arithmetic sequence is 72. The sum of the next three terms is 189. What is the sum of the next three terms after that?

### Seventh Term

In an arithmetic sequence, the first term is twice the fourth term, and the second term is equal to 9 more than the sum of the fifth and sixth terms.

What is the seventh term of the sequence?

### Sum of Squared Terms

The sum of the squares of the first two terms in an arithemetic sequence is 52. The common difference is 2. What are the possible values for the first term?