# In an arithmetic progression, the second term is 8, and the 38th term is 224.

In an arithmetic progression, the second term is 8, and the 38th term is 224. Find the difference of this progression and the sum of its 38 first terms.

We find the first term of the progression from the relation a2 = a1 + d:

a1 = a2 – d.

We find the difference d from the formula for the progression term numbered.

an = a1 + d (n – 1);

an = a2 – d + d (n – 1);

an = a2 + d (n – 1 – 1);

an = a2 + d (n – 2);

d = (аn – a2) / (n – 2) = (224 – 8) / (38 – 2) = 216/36 = 6.

Sum of 38 members of the progression:

S = ((a1 + a38) * n) / 2 = ((a2 – d + a38) * n) / 2 = ((8 – 6 + 224) * 38) / 2 = 4294.

Answer. Difference d = 6, sum S = 4294. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.