Find the sum of the first twenty terms of the arithmetic progression if a1 = 1, a2 = 6.

The difference of the arithmetic progression d is found by the formula:

d = an + 1 – an,

where an + 1 is a member of the progression with number (n + 1), an is a member of the progression preceding the term an + 1.

Let’s calculate the difference of a given arithmetic progression:

d = a2 – a1 = 6 – 1 = 5.

The sum of the first n terms of the arithmetic progression Sn is determined by the formula:

Sn = 1/2 * (a1 + an) * n,

where a1 is the first term, an is the nth term of the progression, n is the number of the nth term.

Then

S20 = 1/2 * (a1 + a20) * 20 = 10 * (a1 + a20).

Find a20:

a20 = a1 + (n – 1) * d = 1 + (20 – 1) * 5 = 96.

Let’s calculate S20:

S20 = 10 * (1 + 96) = 970.

Answer: 970.