# Sequences and Series 1.7 & 1.8 - Math Exams Sequences and Series 1.7 & 1.8 Number sequences, terms, the general term, terminology. In maths, we call a list of numbers in order a sequence. Each number in a sequence is called a term. 4, 8, 12, 16, 20, 24, 28, 32, . . . 1st term 6th term Infinite and finite sequences A sequence can be infinite. That means it continues forever. For example, the sequence of multiples of 10, 10, 20 ,30, 40, 50, 60, 70, 80, 90 . . .

is infinite. We show this by adding three dots at the end. If a sequence has a fixed number of terms it is called a finite sequence. For example, the sequence of two-digit square numbers 16, 25 ,36, 49, 64, 81 is finite. Infinite and finite sequences A sequence can be infinite. That means it continues forever. For example, the sequence of multiples of 10, 10, 20 ,30, 40, 50, 60, 70, 80, 90 . . . is infinite. We show this by adding three dots at the end. If a sequence has a fixed number of terms it is called a finite sequence. For example, the sequence of two-digit square numbers 16, 25 ,36, 49, 64, 81 is finite.

Naming sequences Here are the names of some sequences which you may know already: 2, 4, 6, 8, 10, . . . Even Numbers (or multiples of 2) 1, 3, 5, 7, 9, . . . Odd numbers 3, 6, 9, 12, 15, . . . Multiples of 3 5, 10, 15, 20, 25 . . .

Multiples of 5 1, 4, 9, 16, 25, . . . Square numbers 1, 3, 6, 10,15, . . . Triangular numbers Ascending sequences When each term in a sequence is bigger than the one before the sequence is called an ascending sequence. For example, The terms in this ascending sequence increase in equal steps by adding 5 each time.

2, 7, 12, 17, 22, 27, 32, 37, . . . +5 +5 +5 +5 +5 +5 +5

The terms in this ascending sequence increase in unequal steps by starting at 0.1 and doubling each time. 0.1, 0.2, 0.4, 0.8, 1.6, 3.2, 6.4, 12.8, . . . 2 2 2 2 2 2 2

Descending sequences When each term in a sequence is smaller than the one before the sequence is called a descending sequence. For example, The terms in this descending sequence decrease in equal steps by starting at 24 and subtracting 7 each time. 24, 17, 10, 3, 4, 11, 18, 25, . . . 7 7 7 7 7

7 7 The terms in this descending sequence decrease in unequal steps by starting at 100 and subtracting 1, 2, 3, 100, 99, 97, 94, 90, 85, 79, 72, . . . 1 2 3 4 5

6 7 Describe the following number patterns and write down the next 3 terms: 3, 6,9,12,.... Add 3 3, 6,12, 24,.... Multiply by -2 On your calculator type 3, enter,

times -2, enter, keep pressing enter to generate next terms. 15, 18, 21 48, -96, 192 The general term of a sequence. un u1 (n 1)d un u1r n 1 un 3n 1 1 un 100

2 n Generate the first 4 terms of each of the following sequences. n un 3n 1 u1 3 1 1 3 1 2 u2 3 2 1 6 1 5 u3 3 3 1 9 1 8 u4 3 4 1 12 1 11 2,5,8,11 1

un 100 50, 25,12.5, 6.25 2 1 1 u1 100 50 2 2 1 u2 100 25 2 3 1 u3 100 12.5 2 4

1 u4 100 6.25 2 Using your calculator: Exercise 5A and 5B pages 128, 130