Поезд начал движение от станции. За первую секунду состав сдвинулся на 0,8 м, а каждую следующую секунду он проходил на 0,3 м больше, чем в предыдущую. Сколько метров состав прошёл за первые 6 секунд движения?

The problem describes an arithmetic progression where the first term (a1) is the distance covered in the first second, and the common difference (d) is the increase in distance covered each subsequent second.
a1 = 0.8 m
d = 0.3 m
We need to find the sum of the first 6 terms (S6).
The distance covered in the nth second is given by an = a1 + (n-1)d.
a1 = 0.8
a2 = 0.8 + 0.3 = 1.1
a3 = 1.1 + 0.3 = 1.4
a4 = 1.4 + 0.3 = 1.7
a5 = 1.7 + 0.3 = 2.0
a6 = 2.0 + 0.3 = 2.3
The sum of the first 6 terms is S6 = a1 + a2 + a3 + a4 + a5 + a6 = 0.8 + 1.1 + 1.4 + 1.7 + 2.0 + 2.3 = 9.3 m.
Alternatively, using the formula for the sum of an arithmetic progression: Sn = n/2 * (2a1 + (n-1)d)
S6 = 6/2 * (2*0.8 + (6-1)*0.3)
S6 = 3 * (1.6 + 5*0.3)
S6 = 3 * (1.6 + 1.5)
S6 = 3 * 3.1
S6 = 9.3 m.