Sequence Rules
Maths: Edexcel IGCSE Higher, topic 3.1.1
Sequences - nth Term
What are the 1st, 2nd, 3rd and 10th term in the sequence n² - 3?
1st term: sub in n = 1
2nd term: sub in n = 2
3rd term: sub in n = 3
10th term: sub in n = 10
Sequence so far...
Sequences - Recurrence Relationships
If the 5th term in a sequence is 24, what are the 6th, 7th, and 8th terms if the recurrence relationship is un+1 = un + 4?
This is our recurrence relationship
The 5th term in the sequence is 24
We get this formula for the next term (the 6th)
Evaluate to find the 6th term
Do the same again to find the 7th term
Evaluate
Do the same to find the 8th term
Evaluate
We can see the series goes up by 4 each time
Finding the nth Term - Linear Sequences
What is the nth term formula for the sequence 4, 9, 14, 19, 24, ...?
General formula for a linear sequence is an + b
Look at the difference between each term, it is 5 here
Put this difference in the formula in place of 'a'
Look at the 1st term (n = 1 term)
Substitute n = 1 into the formula which we can see gives 4
Simplify
Solve to find b = -1
Replace b with -1 in the formula and we are done
Test yourself on Sequence Rules
What is the 5th term in the sequence n2 + 5?
What is the 3rd term in the sequence n3 - 12?
What is the general formula for a linear sequence?
What type of sequence is 'an + b' the general formula for?