Odpowiedź:
zad 1
a₁ = 3
a₂ = 2
a₃ = 1
a₃ - a₂ = a₂ - a₁ = r
r = 1 , a₁ = 3
a₁₅ = a₁ + 14r = 3 + 14 * 1 = 3 + 14 = 17
a₃₀ = a₁ + 29r = 3 + 29 * 1 = 3 + 29 = 32
an = a₁ + (n - 1) * r = 3 + (n - 1) * 1 = 3 + (n - 1)
zad 2
a₁ = 3
a₂ = 7
a₃ = 11
a₃ - a₂ = a₂ - a₁ = r
11 - 7 = 7 - 3 = 4
a₁ = 3
r = 4
a₁₁ = a₁ + 10r = 3 + 10 * 4 = 3 + 40 = 43
S₁₁ = (a₁ + a₁₁) * 11/2 = (3 + 43) * 5,5 = 46 * 5,5 = 253
zad 3
a₁ = 4
a₂ = x
a₃ = y
a₄ = 34
a₄ - a₃ = a₃ - a₂ = a₂ - a₁ = r
34 - y = y - x = x - 4
układ równań
34 - y = y - x
y - x = x - 4
x - y - y = - 34
- x - x + y = - 4
x - 2y = - 34 | * 2
- 2x + y = - 4
2x - 4y = - 68
- 2x + y = - 4
dodajemy równania
2x - 2x - 4y + y = - 68 - 4
- 3y = - 72
3y = 72
y = 72 : 3 = 24
- 2x + y = - 4
- 2x + 24 = - 4
- 2x = - 4 - 24
- 2x = - 28
2x = 28
x = 28/2 = 14
wyrazy ciągu
4 , 14 , 24 , 34
x = 14 , y = 24
zad 41
an = 4n - 7
a₁ = 4 * 1 - 7 = 4 - 7 = - 3
a₂ = 4 * 2 - 7 = 8 - 7 = 1
a₃ = 4 * 3 - 7 = 12 - 7 = 5
a₃ - a₂ = 5 - 1 = 4
a₂ - a₁ = 1 - (- 3) = 1 + 3 = 4
r = 4 , a₁ = - 3
a₂₀ = a₁ + 19r = - 3 + 19 * 4 = - 3 + 76 = 73
S₂₀ = (a₁ + a₂₀)/20/2 = (- 3 + 73) * 10 = 70 * 10 = 700
