Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 656

a) 10; 11; 12; …; 99
a₁ = 10
a₂ = 11
d = a₂ – a₁ = 11 – 10 = 1
a_n = 99
a_n = a₁ + d(n – 1)
99 = 10 + 1 · (n – 1)
n – 1 = 99 – 10
n – 1 = 89
n = 90

S_n = $$\frac{a_1 + a_n}{2}$$ · n

S₉₀ = 10 + 99/2 · 90 – 109 · 45 = 4905

б) 100; 101; 102; …; 99
a₁ = 100
a₂ = 101
d = a₂ – a₁ = 101 – 100 = 1
a_n = 100
a_n = a₁ + d(n – 1)
999 = 100 + 1 · (n – 1)
n – 1 = 999 – 100
n – 1 = 899
n = 900

S_n = $$\frac{a_1 + a_n}{2}$$ · n

S₉₀₀ = 100 + 999/2 · 900 = 1099 · 450 = 494550