The first term of an arithmetic sequence is 5. if the25th term is 101 find the common difference?

An arithmetic sequence is one where each term is a constant difference, called the common difference, from the preceding term.  The arithmetic sequence can always be expressed as:

a(n)=a+d(n-1), a=first term, d=common difference, n=term number.

We are given two terms and term numbers, so we can solve for the common difference...

101=5+d(25-1)

101=5+25d-d

101=5+24d

96=24d

d=4

So the common difference is 4.