Page 5 - Number sequence

Question
Consider the sequence: 19; 11; 13; 5; −3; . . .

th
i. Write down the general rule for the n term of the sequence
rd
ii. Hence calculate the 23 term.

Solution
−8 is being added to the previous term to get the next term

Step 2: Then introduce n to −8 so that it is −8n.
Step 3: Term 1: n= 1, then −8(1) + = 19
= 19 + 8
= 27

th
∴ n term = 27 − 8n

th
rd
ii. If the n term = 27 − 8n, then the 23 term = 27 − 8 × 23 = − 157

Using a formula for Arithmetic Sequences

Arithmetic formula is given by = + ( − 1)

Where

is the nth term

is the first term

the nth position of the term in the sequence

is the common difference