Given the nth term for each arithmetic sequence, how to find the common difference and write out the first four terms here? (1) #a_n=2n+7# (2) #a_n=3n-2#
Since every couple of consecutive terms in an arithmetic sequence differ by a common difference, we can subtract any two consecutive terms to find out how distant they are from each other.
So, in the first case, let's consider the
and subtract them:
As for the first four terms, it depends if you consider the first term to be associated with
In other words, you simply have to plug the value of
The second sequence behaves exactly in the same way.