Odpowiedź:
an = 9/5 + 3/5n
a₁ = 9/5 + 3/5 * 1 = 9/5 + 3/5 = 12/5
a₂ = 9/5 + 3/5 * 2 = 9/5 + 6/5 = 15/5
a₃ = 9/5 + 3/5 * 3 = 9/5 + 9/5 = 18/5
a₃ - a₂ = a₂ - a₁
18/5 - 15/5 = 15/5 - 12/5
3/5 = 3/5 , więc jest to ciąg arytmetyczny : a₁ = 12/5 , r = 3/5
a₄₉ = 9/5 + 3/5 * 49 = 9/5 + 147/5 = 9/5 + 29,4 = 1,8 + 29,4 = 31,2
a₉₀ = 9/5 + 3/5 * 90 = 9/5 + 270/5 = 1 4/5 + 54 = 55 4/5 = 55,8
S₄₉ = (a₁ + a₄₉) * 50/2 = (12/5 + 31,2) * 25 = (2 2/5 + 31,2) * 25 =
= (2,4 + 31,2) * 25 = 33,6 * 25 = 840
S₉₀ = (a₁ + a₉₀) * 90/2 = (12/5 + 54 4/5) * 45 = (2,4 + 55,8) * 45 =
= 58,2 * 45= 2619
S₉₀ - S₄₉ = 2619 - 840= 1779
