Question

найдите сумму первых 15 арифметической прогрессии а5=30 а20=85

Answer 1

{ a5 = a1 + 4d = 30
{ a20 = a1 + 19d = 85
Вычитаем из 2 уравнения 1 уравнение.
15d = 55; d = 55/15 = 11/3
a1 = 30 - 4d = 30 - 44/3 = (90-44)/3 = 46/3
a15 = a1 + 14d = 46/3 + 14*11/3 = (46+154)/3 = 200/3
S(15) = (a1+a15)*15/2 = (46/3+200/3)*15/2 = (23+100)*5 = 615