Sequence

A sequence is a list of numbers that follows a rule.

Examples: Find the next two terms of the sequence (a) 3, 7, 11, 15, 19 (b) 1, 4, 9, 16, 25            (c) 1, 1, 2, 3, 5, 8     (d) 81, 27, 9, 3

The nth term of a sequence (T_n or U_n)

The nth term of a sequence is the term from which all other term can be generated using natural  1, 2, 3, 4 …………n

Example:

1. The nth term of a certain sequence is given as Tn = 3X2^n-1

• Write down the first three terms of the sequence
• What is the 10^th tern of the sequence

Solution

T_n= 3 x 2^n-1

• The first term T₁ = 3 x 2^o = 3

The second term T₂ = 3 x 2¹ = 6

The Second term T₃= 3 x 2² = 12

The first three terms are 3, 6, 12

• The 10^th T₁₀ = 3 x 2⁹= 1536

2. Find the n^th term of the sequence 2, 6, 10, 14, 18

Solution

Since the rule is add 4 each time.  So we try 4n – 2 or 4n + 2                                               when n=1, 4n-2 = 4-2 =2.

When n = 2, 4n-2=8-2=6

When n=3 4n-2=12-2 = 10

When n=4, 4n – 2 = 16 – 2 = 14

When n = 5, 4n-2 = 20-2 = 18.   Tn = 4n-2

Exercise: Find the first three terms of the sequence with n^th term U_n=3n²

State the nth term of the sequence 2, 5, 8, 11, 14