In the figure below we are given two terms of an arithmetic sequence, namely and .
First, let’s find the common difference.
The difference between 52 and 16 is 36.
There are four ‘steps’ between and . So we divide the difference into four.
The common difference between consecutive terms is .
We can find the common difference using a calculation like this:
Since we don’t know the first term in the sequence, we can either
- figure it out
- use a different technique.
Let’s use a different technique.
Since the common difference is 9, we know that the general term is . We don’t yet know the value of .
To calculate , let’s substitute one of our known terms: . Here, the term is 16 and it is in the third place, so .
We can check this expression with the other known term. Let’s make sure that this expression gives us 52 for the seventh term.