## SAT SUBJECT TEST MATH LEVEL 1

## MISCELLANEOUS TOPICS

## CHAPTER 18

Sequences

### ARITHMETIC SEQUENCES

An ** arithmetic sequence** is a sequence such as 5, 8, 11, 14, 17, . . . in which the difference between any two consecutive terms is the same. In this sequence, the difference is 3 (8 – 5 = 3; 11 – 8 = 3; 14 – 11 = 3, . . .). An easy way to find the

*n*th term of such a sequence is to start with the first term and add the common difference

*n*– 1 times. Here, the 5th term is 17 which can be obtained by taking the first term, 5, and adding the common difference, 3, four times: 5 + 4(3) = 17. In the same way, the 100th term is 5 + 99(3) = 5 + 297 = 302.

**Key Fact Q2**

**If a_{1}, a_{2}, a_{3}, . . . is an arithmetic sequence whose common difference is d, then a_{n}** =

**+**

*a*_{1}**(**–

*n***1)**

*d*.**EXAMPLE 4:** If the 8th term of an arithmetic sequence is 10 and the 20th term is 58, what is the first term?

Use KEY FACT Q2 twice and subtract:

Then

10 = *a*_{1} + 7*d* = *a*_{1} + 7(4) = *a*_{1} + 28 *a*_{1} = –18