An arithmetic progression is given for which a4 = 18, a17 = 213. find the difference of the progression

Take the members of the progression from 4 to 17 and write down their sum;
The sum of n members of an arithmetic progression is:

a1 + an 2 x a1 + d x (n – 1)
Sn = ———- x n = ———————– x n;
2 2

a1 = a4 = 18;
an = a17 = 213;

n = 14;
d is the difference;

18 + 213 2 x 18 + d x (14 – 1)
Sn = ———- x 14 = ———————– x 14;
2 2
We shorten the expression:
231 = 2 x 18 + 13d;

13d = 195;
d = 15;
Answer: The difference of the arithmetic progression d = 15;