Question

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

Answer 1

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.

Answer 2

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