Question 1154916
arithmetic sequence is An = A1 + (n-1) * d
when n = 5, A5 = A1 + (5-1) * d
when n = 21, A21 = A1 + 21-1) * d
simplify these equations to get:
A5 = A1 + 4d
A21 = A1 + 20d
since A5 = 2.25 and A21 = 6.25, you get:
2.25 = A1 + 4d
6.25 = A1 + 20d
subtract the second equation from the first to get:
4.00 = 16d
solve for d to get:
d = 4.00 / 16 = .25


when d = .25 and n = 5 and A5 = 2.25, you get:
2.25 = A1 + (5-1) * .25
simplify to get:
2.25 = A1 + 4 * .25
simplify further to get:
2.25 = A1 + 1
solve for A1 to get A1 = 1.25


when d = .25 and n = 21 and A21 = 6.25, you get:
6.25 = A1 + (21-1) * .25
simplify to get:
6.25 = A1 + 20 * .25
simplify further to get:
6.25 = A1 + 5
solve for A1 to get A1 = 1.25


d = .25 is the common difference.
both equations are true when d = .25
the general equation is An = A1 + (n-1) * d
d = .25 should be the answer to your question.