Gillian has a pay-as-you-go mobile phone contract and she is trying to work out how much money she has spent on texts this week.
The cost of 1 text message is 5p.
You would make a table of values for up to 6 texts showing the cost in pence as below.
Now, we need to find a formula that will help us find the cost of any number of texts.
From the table above, you should notice that the cost increases by 5 each time.
The formula is
Gillian has sent 87 texts this week. How much money has Gillian spent on texts this week?
Cost (in pence) = 5 x number of texts
This can be re-written as:
Gillian sent 87 texts this week. We can now use this formula to calculate the cost.
1, 4, 7, 10 is a sequence starting with 1.
You get the next term by adding 3 to the previous term.
You are often asked to find a formula for the nth term.
Find the nth term.
To do this, we first of all find the difference between each term. This tells us part of our formula:
When we substitute into this formula, we find that it doesn’t work as , but the first term is 1.
Now all we have to do is subtract 2.
Now try this for some other terms to make sure your rule works:
Now we have established our formula:
This method will always work for sequences where the difference between terms stays the same.
Find the nth term in the sequence 1, 5, 9, 13.
The formula for the sequence is .