     Home Arithmetic Sequences Geometric Sequences Arithmetic Series Geometric Series Sigma Notation Mathematical Induction Review&Test UNIT 10  :  SEQUENCES AND SERIES

LESSON 3: ARITHMETIC SERIES

Arithmetic Series:

Recall a sequence such as –2, 3, 8, 13, … is called an Arithmetic Sequence.  These sequences have the following properties.

·        Terms are denoted as t1 , t2 , t3 , referring  to term1, term 2, term 3 …

·        The difference between successive terms is constant.  ie  t2 – t1 = t3 – t2 = t4 – t3  etc

·        This difference is called the common difference and denoted using the letter d.  Here d = 5.

·        The first term is denoted using the letter a.  Here a = -2.

·        Successive terms are found by adding the common difference, d, to the preceding term.  Hence t5 = 13 + 5 = 18 etc.

·        The formula for the general term or nth term is   tn = a + (n – 1)d Definition: The sum of the terms of an arithmetic sequence is an Arithmetic Series.  Example 1: Given the first few terms.

For the arithmetic series below, above, find  t11, the general term tn and the sum of 40 terms S40. Solution:

 a = 1 d = 3 n = 11 tn = ? S40 = ? Example 2: Given the first and last terms. a = - 3 d = - 4 tn = - 219 n = ? Sn = ?

Solution: Example 3: Given two terms.

The fourth and seventh terms of an arithmetic series are 8 and 17 respectively.  Find a, d  and S26.

Solution: 