How do you find both the 1st term of an arithmetic sequence and the common difference?
for example, when the seventh term in the sequence is 5 and the sum of the first 16 terms is 20

An arithmetic sequence is one in which consecutive terms differ by some fixed number. Recursively, such a sequence is given by

where is the common difference between terms.

Using this definition, you can express any term of the sequence in terms of , since

and so on down to the explicit rule,

The sum of the first terms, , of such a sequence is

or, using the explicit rule,

Now, given and , we have

which you can solve to get