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

First term a1 = 5

25th term = a1 + 24d = 101 (where d = common difference)

5 + 24d = 101

24d = 96

d = 96/24 = 4

common difference = 4

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.